diff --git a/documentation/leo/08_auction.md b/documentation/leo/08_auction.md index 4f7d0e8d7..11a5b9f74 100644 --- a/documentation/leo/08_auction.md +++ b/documentation/leo/08_auction.md @@ -20,110 +20,70 @@ We make following assumptions about the auction: Under this model, we require that: - Bidders do not learn any information about the value of other bids. -### Auction Flow +## Auction Flow + The auction is conducted in a series of stages. - **Bidding**: In the bidding stage, bidders submit bids to the auctioneer. They do so by invoking the `place_bid` function. - **Resolution**: In the resolution stage, the auctioneer resolves the bids in the order they were received. The auctioneer does so by invoking the `resolve` function. The resolution process produces a single winning bid. - **Finishing**: In this stage, the auctioneer finishes the auction by invoking the `finish` function. This function returns the winning bid to the bidder, which the bidder can then use to claim the item. - ## Language Features and Concepts - `record` declarations - `assert_eq` - record ownership -## Setup - -### 1. Install Leo -Follow the [**Leo Installation Instructions**](./01_installation.md) - -### 2. Download the auction example code -Clone the source code for the auction example from [Github](https://github.com/AleoHQ/workshop/tree/master/auction). - ## How to Run -### Generating Accounts -The `program.json` file contains a private key and address. -This is the account that will be used to sign transactions and is checked for record ownership. -When executing programs as different parties, be sure to set the `private_key` and `address` fields in `program.json` to the appropriate values. -See `./run.sh` for an example of how to run the program as different parties. - -Go to [**aleo.tools**](https://aleo.tools) to generate new accounts. +Follow the [Leo Installation Instructions](https://developer.aleo.org/leo/installation). -The web interface is powered by the [Aleo SDK](https://github.com/AleoHQ/sdk) and can be run locally. +This auction program can be run using the following bash script. Locally, it will execute Leo program functions to conduct, bid, and close a three party auction. -### Using an input file. -1. Modify `inputs/auction.in` with the desired inputs. -2. Run ```bash -leo run +cd auction +./run.sh ``` +The `.env` file contains a private key and address. This is the account that will be used to sign transactions and is checked for record ownership. When executing programs as different parties, be sure to set the `private_key` field in `.env` to the appropriate value. You can check out how we've set things up in `./run.sh` for a full example of how to run the program as different parties. + +## Walkthrough * [Step 0: Initializing the Auction](#step0) * [Step 1: The First Bid](#step1) * [Step 2: The Second Bid](#step2) * [Step 3: Select the Winner](#step3) - - - ## Step 0: Initializing the Auction -You can use the provided accounts or [generate your own](#accounts) +The three parties we'll be emulating are as follows: ```markdown -Bidder 1: - Private Key APrivateKey1zkpG9Af9z5Ha4ejVyMCqVFXRKknSm8L1ELEwcc4htk9YhVK - Address aleo1yzlta2q5h8t0fqe0v6dyh9mtv4aggd53fgzr068jvplqhvqsnvzq7pj2ke - -Bidder 2: - Private Key APrivateKey1zkpAFshdsj2EqQzXh5zHceDapFWVCwR6wMCJFfkLYRKupug - Address aleo1esqchvevwn7n5p84e735w4dtwt2hdtu4dpguwgwy94tsxm2p7qpqmlrta4 - -Auctioneer: - Private Key APrivateKey1zkp5wvamYgK3WCAdpBQxZqQX8XnuN2u11Y6QprZTriVwZVc - Address aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh +Bidder 1 Private Key: +APrivateKey1zkpG9Af9z5Ha4ejVyMCqVFXRKknSm8L1ELEwcc4htk9YhVK +Bidder 1 Address: +aleo1yzlta2q5h8t0fqe0v6dyh9mtv4aggd53fgzr068jvplqhvqsnvzq7pj2ke + +Bidder 2 Private Key: +APrivateKey1zkpAFshdsj2EqQzXh5zHceDapFWVCwR6wMCJFfkLYRKupug +Bidder 2 Address: +aleo1esqchvevwn7n5p84e735w4dtwt2hdtu4dpguwgwy94tsxm2p7qpqmlrta4 + +Auctioneer Private Key: +APrivateKey1zkp5wvamYgK3WCAdpBQxZqQX8XnuN2u11Y6QprZTriVwZVc +Auctioneer Address: +aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh ``` -Swap in the private key and address of the first bidder to program.json. - -```jsonld -{ - "program": "auction.aleo", - "version": "0.0.0", - "description": "A sealed bid auction", - "development": { - "private_key": "APrivateKey1zkpG9Af9z5Ha4ejVyMCqVFXRKknSm8L1ELEwcc4htk9YhVK", - "address": "aleo1yzlta2q5h8t0fqe0v6dyh9mtv4aggd53fgzr068jvplqhvqsnvzq7pj2ke" - }, - "license": "MIT" -} -``` +## Step 1: The First Bid +Have the first bidder place a bid of 10. -## Step 1: The First Bid +Swap in the private key and address of the first bidder to `.env`. -Have the first bidder place a bid of 10. - -```javascript=19 - // Returns a new bid. - // - `bidder` : The address of the account that placed the bid. - // - `amount` : The amount of the bid. - // Requires that `bidder` matches the function caller. - // The owner of the record is set to the entity responsible for running the auction (auction runner). - // The address of the auction runner is aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh. - transition place_bid(bidder: address, amount: u64) -> Bid { - // Ensure the caller is the auction bidder. - console.assert_eq(self.caller, bidder); - // Return a new 'Bid' record for the auction bidder. - return Bid { - owner: aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh, - bidder: bidder, - amount: amount, - is_winner: false, - }; - } +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpG9Af9z5Ha4ejVyMCqVFXRKknSm8L1ELEwcc4htk9YhVK +" > .env ``` Call the `place_bid` program function with bidder 1 and `10u64` arguments. @@ -136,8 +96,14 @@ leo run place_bid aleo1yzlta2q5h8t0fqe0v6dyh9mtv4aggd53fgzr068jvplqhvqsnvzq7pj2k Have the second bidder place a bid of 90. +Swap in the private key of the second bidder to `.env`. -Swap in the private key and address of the second bidder to program.json. +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpAFshdsj2EqQzXh5zHceDapFWVCwR6wMCJFfkLYRKupug +" > .env +``` Call the `place_bid` program function with bidder 2 and `90u64` arguments. @@ -149,77 +115,45 @@ leo run place_bid aleo1esqchvevwn7n5p84e735w4dtwt2hdtu4dpguwgwy94tsxm2p7qpqmlrta Have the auctioneer select the winning bid. -```javascript=38 - // Returns the winning bid. - // - `first` : The first bid. - // - `second` : The second bid. - // Requires that the function caller is the auction runner. - // Assumes that the function is invoked only after the bidding period has ended. - // In the event of a tie, the first bid is selected. - transition resolve(first: Bid, second: Bid) -> Bid { - // Ensure the caller is the auctioneer. - assert_eq(self.caller, aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh); - // Resolve the winner of the auction. - if (first.amount >= second.amount) { - return first; - } else { - return second; - } - } -``` +Swap in the private key of the auctioneer to `.env`. -Swap in the private key and address of the auctioneer to program.json. +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp5wvamYgK3WCAdpBQxZqQX8XnuN2u11Y6QprZTriVwZVc +" > .env +``` Provide the two `Bid` records as input to the `resolve` transition function. ```bash leo run resolve "{ - owner: aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh.private, - bidder: aleo1yzlta2q5h8t0fqe0v6dyh9mtv4aggd53fgzr068jvplqhvqsnvzq7pj2ke.private, - amount: 10u64.private, - is_winner: false.private, - _nonce: 4668394794828730542675887906815309351994017139223602571716627453741502624516group.public - }" "{ - owner: aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh.private, - bidder: aleo1esqchvevwn7n5p84e735w4dtwt2hdtu4dpguwgwy94tsxm2p7qpqmlrta4.private, - amount: 90u64.private, - is_winner: false.private, - _nonce: 5952811863753971450641238938606857357746712138665944763541786901326522216736group.public - }" + owner: aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh.private, + bidder: aleo1yzlta2q5h8t0fqe0v6dyh9mtv4aggd53fgzr068jvplqhvqsnvzq7pj2ke.private, + amount: 10u64.private, + is_winner: false.private, + _nonce: 4668394794828730542675887906815309351994017139223602571716627453741502624516group.public +}" "{ + owner: aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh.private, + bidder: aleo1esqchvevwn7n5p84e735w4dtwt2hdtu4dpguwgwy94tsxm2p7qpqmlrta4.private, + amount: 90u64.private, + is_winner: false.private, + _nonce: 5952811863753971450641238938606857357746712138665944763541786901326522216736group.public +}" ``` ## Step 4: Finish the Auction -Have the auctioneer finish the auction. - -```javascript=55 - // Returns ownership of the bid to bidder. - // - `bid` : The winning bid. - // Requires that the function caller is the auction runner. - // Assumes that the function is invoked only after all bids have been resolved. - transition finish(bid: Bid) -> Bid { - // Ensure the caller is the auctioneer. - console.assert_eq(self.caller, aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh); - // Return 'is_winner' as 'true' in the winning 'Bid'. - return Bid { - owner: bid.bidder, - bidder: bid.bidder, - amount: bid.amount, - is_winner: true, - }; - } -``` - Call the `finish` transition function with the winning `Bid` record. ```bash leo run finish "{ - owner: aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh.private, - bidder: aleo1esqchvevwn7n5p84e735w4dtwt2hdtu4dpguwgwy94tsxm2p7qpqmlrta4.private, - amount: 90u64.private, - is_winner: false.private, - _nonce: 5952811863753971450641238938606857357746712138665944763541786901326522216736group.public - }" + owner: aleo1fxs9s0w97lmkwlcmgn0z3nuxufdee5yck9wqrs0umevp7qs0sg9q5xxxzh.private, + bidder: aleo1esqchvevwn7n5p84e735w4dtwt2hdtu4dpguwgwy94tsxm2p7qpqmlrta4.private, + amount: 90u64.private, + is_winner: false.private, + _nonce: 5952811863753971450641238938606857357746712138665944763541786901326522216736group.public +}" ``` - +Congratulations! You've run a private auction. We recommend going to [aleo.tools](https://aleo.tools) to generate new accounts and trying the same commands with those addresses. diff --git a/documentation/leo/10_basic_bank.md b/documentation/leo/10_basic_bank.md new file mode 100644 index 000000000..ff50811d5 --- /dev/null +++ b/documentation/leo/10_basic_bank.md @@ -0,0 +1,114 @@ +## Summary + +This program implements a bank that issues tokens to users and allows users to deposit tokens to accrue simple interest on their deposits. + +### User Flow +1. The bank issues users tokens via the `issue` function. +2. A user deposits tokens via the `deposit` function. +3. Upon a user's request to withdraw, the bank calculates the appropriate amount of compound interest and pays the user the principal and interest via the `withdraw` function. + +Note that the program can be easily extended to include addition features such as a `transfer` function, which would allow users to transfer tokens to other users. + +## Bugs + +You may have already guessed that this program has a few bugs. We list some of them below: +- `withdraw` can only be invoked by the bank. A malicious bank could lock users' tokens by not invoking `withdraw`. +- `withdraw` fails if the sum of the interest and principal is greater than the user's balance. +- User's can increase their principal by depositing tokens multiple times, including immediately before withdrawl. +- Integer division rounds down; if the calculated interest is too small, then it will be rounded down to zero. + +Can you find any others? + +## Language Features and Concepts +- `record` declarations +- `assert_eq` +- core functions, e.g. `BHP256::hash` +- record ownership +- loops and bounded iteration +- mappings +- finalize + +## How to Run + +Follow the [Leo Installation Instructions](https://developer.aleo.org/leo/installation). + +This basic bank program can be run using the following bash script. Locally, it will execute Leo program functions to issue, deposit, and withdraw tokens between a bank and a user. + +```bash +cd basic_bank +./run.sh +``` + +The `.env` file contains a private key and address. This is the account that will be used to sign transactions and is checked for record ownership. When executing programs as different parties, be sure to set the `private_key` field in `.env` to the appropriate value. You can check out how we've set things up in `./run.sh` for a full example of how to run the program as different parties. + +## Walkthrough + +* [Step 0: Issue Tokens](#issue) +* [Step 1: Deposit Tokens](#deposit) +* [Step 2: Wait](#wait) +* [Step 3: Withdraw Tokens](#withdraw) + +## Issue Tokens + +We will be playing the role of two parties. + +```bash +The private key and address of the bank. +private_key: APrivateKey1zkpHtqVWT6fSHgUMNxsuVf7eaR6id2cj7TieKY1Z8CP5rCD +address: aleo1t0uer3jgtsgmx5tq6x6f9ecu8tr57rzzfnc2dgmcqldceal0ls9qf6st7a + +The private key and address of the user. +private_key: APrivateKey1zkp75cpr5NNQpVWc5mfsD9Uf2wg6XvHknf82iwB636q3rtc +address: aleo1zeklp6dd8e764spe74xez6f8w27dlua3w7hl4z2uln03re52egpsv46ngg +``` + +Let's make some bank transactions. We'll take the role of the bank and issue 100 tokens to the user. We swap the private key into `.env` and run the `issue` transition function. The inputs are simply the recipient of the issuance and the amount. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpHtqVWT6fSHgUMNxsuVf7eaR6id2cj7TieKY1Z8CP5rCD +" > .env + +leo run issue aleo1zeklp6dd8e764spe74xez6f8w27dlua3w7hl4z2uln03re52egpsv46ngg 100u64 +``` + +## Deposit Tokens + +Now, let's have the user deposit 50 of their tokens with the bank. We'll take the role of the user and call the deposit function, having the user use the output record that was issued to them by the bank. The inputs are the output record from the `issue` transition and the amount the user wishes to deposit. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp75cpr5NNQpVWc5mfsD9Uf2wg6XvHknf82iwB636q3rtc +" > .env + +leo run deposit "{ + owner: aleo1zeklp6dd8e764spe74xez6f8w27dlua3w7hl4z2uln03re52egpsv46ngg.private, + amount: 100u64.private, + _nonce: 4668394794828730542675887906815309351994017139223602571716627453741502624516group.public +}" 50u64 +``` + +You'll see that the output contains a new private record belonging to the user with 50 credits, and a finalize `deposit` function taking the arguments (bank address, amount) that will update a public mapping with 50 credits. This information is queryable on-chain. + +## Wait + +With the 50 token deposit, let's say 15 periods of time pass with compounding interest at a rate of 12.34% on the principal amount. + +You can run the calculation yourself, it comes out to 266 tokens accrued using those numbers. + +## Withdraw Tokens + +Now, let's have the bank withdraw all tokens after 15 periods. Let's switch to the bank role, and call the `withdraw` transition function. The inputs are the recipient's address, amount, rate, and periods. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpHtqVWT6fSHgUMNxsuVf7eaR6id2cj7TieKY1Z8CP5rCD +" > .env + +leo run withdraw aleo1zeklp6dd8e764spe74xez6f8w27dlua3w7hl4z2uln03re52egpsv46ngg 50u64 1234u64 15u64 +``` + +You'll see here the withdrawal function creates a new private record for the user containing all 266 withdrawn tokens, and then calls the finalize `withdraw` function with arguments (address, amount), which will update the public balance of the bank back to 0. The public mapping will be queryable on-chain. \ No newline at end of file diff --git a/documentation/leo/11_tictactoe.md b/documentation/leo/11_tictactoe.md new file mode 100644 index 000000000..e488d6596 --- /dev/null +++ b/documentation/leo/11_tictactoe.md @@ -0,0 +1,86 @@ +--- +id: tictactoe +title: A standard game of Tic-Tac-Toe in Leo. +--- + +## Summary + +We can play a standard game of Tic-Tac-Toe in Leo. I think we all know what a tictactoe board looks like: + +⭕ ❕ ⭕ ❕ ❌ + +➖ ➕ ➖ ➕ ➖ + +⭕ ❕ ⁣❌ ❕ ⭕ + +➖ ➕ ➖ ➕ ➖ + +❌ ❕ ❌ ❕ ⭕ + +## Representing State +Leo allows users to define composite data types with the `struct` keyword. +The game board is represented by a struct called `Board`, which contains three `Row`s. An alternative representation would be to use an array, however, these are not yet supported in Leo. + +## Language Features +- `struct` declarations +- conditional statements +- early termination. Leo allows users to return from a function early using the `return` keyword. + +## How to Run + +Follow the [Leo Installation Instructions](https://developer.aleo.org/leo/installation). + +This tictactoe program can be run using the following bash script. Locally, it will execute Leo program functions to create and play a game of Tic Tac Toe. + +```bash +cd tictactoe +./run.sh +``` + +## Walkthrough + +* [Step 0: Create a new board.](#step0) +* [Step 1: Player 1 makes the first move.](#step1) +* [Step 2: Player 2 makes the second move.](#step2) +* [Step 3: Player 1 makes the third move.](#step3) +* [Step 4: and so on...](#step4) + +## Create a new board. + +We generate the board, and then the player take turns executing the transition function make_move. + +The inputs to the function are the player number, row position, column position, and the previous state of the board. + +The output provided is the new state of the board and an evaluation of who won the game. 0u8 as the evaluation output means a draw if the board is complete or that the game is not yet over. + +```bash +leo run new +``` +## Player 1 makes a move. + +Have player 1 make the first move. + +```bash +leo run make_move 1u8 1u8 1u8 "{ r1: { c1: 0u8, c2: 0u8, c3: 0u8 }, r2: { c1: 0u8, c2: 0u8, c3: 0u8 }, r3: { c1: 0u8, c2: 0u8, c3: 0u8 } }" +``` + +## Player 2 makes a move. + +Have player 2 make the second move. + +```bash +leo run make_move 2u8 2u8 2u8 "{ r1: { c1: 1u8, c2: 0u8, c3: 0u8 }, r2: { c1: 0u8, c2: 0u8, c3: 0u8 }, r3: { c1: 0u8, c2: 0u8, c3: 0u8 } }" +``` + +## Player 1 makes a move. + +Have player 1 make the third move. + +```bash +leo run make_move 1u8 3u8 1u8 "{ r1: { c1: 1u8, c2: 0u8, c3: 0u8 }, r2: { c1: 0u8, c2: 2u8, c3: 0u8 }, r3: { c1: 0u8, c2: 0u8, c3: 0u8 } }" +``` + +## and so on... + +If you follow the run script till the end, you'll see the players make a draw, with an output of `0u64`. + diff --git a/documentation/leo/12_vote.md b/documentation/leo/12_vote.md new file mode 100644 index 000000000..d060247bc --- /dev/null +++ b/documentation/leo/12_vote.md @@ -0,0 +1,140 @@ +--- +id: vote +title: A general vote program. +--- + +## Summary + +`vote.leo` is a general vote program. + +Anyone can issue new proposals, proposers can issue tickets to the voters, and voters can vote without exposing their identity. + +This example is inspired by the [aleo-vote](https://github.com/zkprivacy/aleo-vote) example written by the Aleo community. + +## Noteworthy Features + +Voter identity is concealed by privately passing a voter's ballot into a function. +Proposal information and voting results are revealed using the public `mapping` datatype in Leo. + +## How to Run + +Follow the [Leo Installation Instructions](https://developer.aleo.org/leo/installation). + +This vote program can be run using the following bash script. Locally, it will execute Leo program functions to create proposals, create tickets, and make votes. + +```bash +cd vote +./run.sh +``` + +The `.env` file contains a private key and address. This is the account that will be used to sign transactions and is checked for record ownership. When executing programs as different parties, be sure to set the `private_key` field in `.env` to the appropriate value. You can check out how we've set things up in `./run.sh` for a full example of how to run the program as different parties. + +## Walkthrough + +* [Functions](#functions) +* [Step 0: Create a Proposal](#step0) +* [Step 1: Voter 1 issues a ticket and makes a vote](#step1) +* [Step 2: Voter 2 issues a ticket and makes a vote](#step2) +* [Step 3: How votes are tallied](#step3) + +## Functions + +### Propose + +Anyone can issue a new proposal publicly by calling `propose` function. + +### Create Ticket + +Proposers can create new tickets for proposed proposals. + +Ticket is a record with `owner` and `pid`, it can be used to vote for the specific proposal - `pid`, and can only be used(voted) by the ticket `owner`. + +### Vote + +A ticket owner can use their ticket record to vote `agree` / `disagree` with the specific proposal - `pid`. Since the ticket record can be used as an input privately, the voter's privacy is protected. + +## Create a Proposal + +We will be playing the role of three parties. + +```bash +The private key and address of the proposer. +private_key: APrivateKey1zkp8wKHF9zFX1j4YJrK3JhxtyKDmPbRu9LrnEW8Ki56UQ3G +address: aleo1rfez44epy0m7nv4pskvjy6vex64tnt0xy90fyhrg49cwe0t9ws8sh6nhhr + +The private key and address of voter 1. +private_key: APrivateKey1zkpHmSu9zuhyuCJqVfQE8p82HXpCTLVa8Z2HUNaiy9mrug2 +address: aleo1c45etea8czkyscyqawxs7auqjz08daaagp2zq4qjydkhxt997q9s77rsp2 + +The private key and address of voter 2. +private_key: APrivateKey1zkp6NHwbT7PkpnEFeBidz5ZkZ14W8WXZmJ6kjKbEHYdMmf2 +address: aleo1uc6jphye8y9gfqtezrz240ak963sdgugd7s96qpuw6k7jz9axs8q2qnhxc +``` +Let's propose a new ballot. Take on the role of the proposer and run the propose transition function. We've provided the necessary information as inputs to the `propose` function. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp8wKHF9zFX1j4YJrK3JhxtyKDmPbRu9LrnEW8Ki56UQ3G +" > .env + +leo run propose "{ + title: 2077160157502449938194577302446444field, + content: 1452374294790018907888397545906607852827800436field, + proposer: aleo1rfez44epy0m7nv4pskvjy6vex64tnt0xy90fyhrg49cwe0t9ws8sh6nhhr +}" +``` + +You'll see that the output generates a new record with the proposal information and sets a public mapping with the proposal id as an argument input. The public mapping will be queryable on-chain. + +## Voter 1 makes a vote + +Let's create a new private ticket to make a vote. Take on the role of voter 1 and run the `new_ticket` transition. The inputs take a unique ticket ID and the voter's public address. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpHmSu9zuhyuCJqVfQE8p82HXpCTLVa8Z2HUNaiy9mrug2 +" > .env + +leo run new_ticket 2264670486490520844857553240576860973319410481267184439818180411609250173817field aleo1c45etea8czkyscyqawxs7auqjz08daaagp2zq4qjydkhxt997q9s77rsp2 +``` + +You'll see a new private ticket created belonging to the owner, and a public mapping in the vote program to track the ID of that ticket. + +Voter 1 can now vote privately on their ticket. Call the agree or disagree transition function, which takes the voter's ticket output as the input. + +```bash +leo run agree "{ + owner: aleo1c45etea8czkyscyqawxs7auqjz08daaagp2zq4qjydkhxt997q9s77rsp2.private, + pid: 2264670486490520844857553240576860973319410481267184439818180411609250173817field.private, + _nonce: 1738483341280375163846743812193292672860569105378494043894154684192972730518group.public +}" +``` + +## Voter 2 makes a vote + +Let's create a new private ticket for voter 2. Take on the role of voter 1 and run the `new_ticket` transition. The inputs take a unique ticket ID and the voter's public address. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp6NHwbT7PkpnEFeBidz5ZkZ14W8WXZmJ6kjKbEHYdMmf2 +" > .env + +leo run new_ticket 2158670485494560943857353240576760973319410481267184429818180411607250143681field aleo1uc6jphye8y9gfqtezrz240ak963sdgugd7s96qpuw6k7jz9axs8q2qnhxc +``` + +Voter 2 can now vote privately on their ticket. Call the agree or disagree transition function, which takes the voter's ticket output as the input. + +```bash +leo run disagree "{ + owner: aleo1uc6jphye8y9gfqtezrz240ak963sdgugd7s96qpuw6k7jz9axs8q2qnhxc.private, + pid: 2158670485494560943857353240576760973319410481267184429818180411607250143681field.private, + _nonce: 6511154004161574129036815174288926693337549214513234790975047364416273541105group.public +}" +``` + +## How votes are tallied + +Votes on the ticket are private. But the sum total of the agreements and disagreements are shown on-chain in the public mapping. You can query this data on-chain. \ No newline at end of file diff --git a/documentation/leo/13_token.md b/documentation/leo/13_token.md new file mode 100644 index 000000000..030fa297f --- /dev/null +++ b/documentation/leo/13_token.md @@ -0,0 +1,141 @@ +--- +id: token +title: A transparent & shielded custom token in Leo. +--- + +## Summary + +A transparent & shielded custom token in Leo. + +## How to Run + +Follow the [Leo Installation Instructions](https://developer.aleo.org/leo/installation). + +This token program can be run using the following bash script. Locally, it will execute Leo program functions to mint and transfer tokens publicly and privately. + + +```bash +cd token +./run.sh +``` + +The `.env` file contains a private key and address. This is the account that will be used to sign transactions and is checked for record ownership. When executing programs as different parties, be sure to set the `private_key` field in `.env` to the appropriate value. You can check out how we've set things up in `./run.sh` for a full example of how to run the program as different parties. + +## Walkthrough + +* [Step 0: Public Mint](#step0) +* [Step 1: Private Mint](#step1) +* [Step 2: Public Transfer](#step2) +* [Step 3: Private Transfer](#step3) +* [Step 4: Public to Private Transfer](#step4) +* [Step 5: Private to Public Transfer](#step5) + +We'll be conducting a transfer between two parties. + +```bash +The private key and address of Alice. +private_key: APrivateKey1zkp1w8PTxrRgGfAtfKUSq43iQyVbdQHfhGbiNPEg2LVSEXR +address: aleo13ssze66adjjkt795z9u5wpq8h6kn0y2657726h4h3e3wfnez4vqsm3008q + +The private key and address of Bob. +private_key: APrivateKey1zkpFo72g7N9iFt3JzzeG8CqsS5doAiXyFvNCgk2oHvjRCzF +address: aleo17vy26rpdhqx4598y5gp7nvaa9rk7tnvl6ufhvvf4calsrrqdaqyshdsf5z +``` + +## Public Mint + +Let's play Alice. Swap in her private key and publicly mint 100 tokens. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp1w8PTxrRgGfAtfKUSq43iQyVbdQHfhGbiNPEg2LVSEXR +" > .env + +leo run mint_public aleo13ssze66adjjkt795z9u5wpq8h6kn0y2657726h4h3e3wfnez4vqsm3008q 100u64 +``` + +You can see the output of the finalize function of `mint_public`, which takes the arguments Alice's address and the amount of tokens to mint publicly. This information is shown on-chain and can be queried on a network. + +## Private Mint + +Now let's privately mint 100 tokens for Bob. Switch to Bob's private key and privately mint 100 tokens for Bob. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpFo72g7N9iFt3JzzeG8CqsS5doAiXyFvNCgk2oHvjRCzF +" > .env + +leo run mint_private aleo17vy26rpdhqx4598y5gp7nvaa9rk7tnvl6ufhvvf4calsrrqdaqyshdsf5z 100u64 +``` + +The output is a private record. + +## Public Transfer + +Let's publicly transfer 10 tokens from Alice to Bob. Swap the private key back to Alice and call the public transfer transition. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp1w8PTxrRgGfAtfKUSq43iQyVbdQHfhGbiNPEg2LVSEXR +" > .env + +leo run transfer_public aleo17vy26rpdhqx4598y5gp7nvaa9rk7tnvl6ufhvvf4calsrrqdaqyshdsf5z 10u64 +``` + +Again, we see the arguments used for the finzalize function of `transfer_public` - Alice's address, Bob's address, and the amount to transfer. The public mapping will be queryable on-chain. + +## Private Transfer + +Let's privately transfer 20 tokens from Bob to Alice. Switch to Bob's private key and call the private transfer transition. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpFo72g7N9iFt3JzzeG8CqsS5doAiXyFvNCgk2oHvjRCzF +" > .env + +leo run transfer_private "{ + owner: aleo17vy26rpdhqx4598y5gp7nvaa9rk7tnvl6ufhvvf4calsrrqdaqyshdsf5z.private, + amount: 100u64.private, + _nonce: 6586771265379155927089644749305420610382723873232320906747954786091923851913group.public +}" aleo13ssze66adjjkt795z9u5wpq8h6kn0y2657726h4h3e3wfnez4vqsm3008q 20u64 +``` + +The output of `transfer_private` is a record owned by Bob less the 20 tokens he privately transferred to Alice, and a record owned by Alice with the 20 tokens Bob transferred to Alice. + +## Public to Private Transfer + +Let's convert 30 of Alice's public tokens into 30 private tokens for Bob. Switch the private key back to Alice. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp1w8PTxrRgGfAtfKUSq43iQyVbdQHfhGbiNPEg2LVSEXR +" > .env + +leo run transfer_public_to_private aleo17vy26rpdhqx4598y5gp7nvaa9rk7tnvl6ufhvvf4calsrrqdaqyshdsf5z 30u64 +``` + +When calling `transfer_public_to_private`, we see the finalize function with the arguments to modify Alice's public token mapping (address, amount), and a private record created that's owned by Bob and contains 110 tokens. + +## Private to Public Transfer + +Let's convert 40 of Bob's private tokens into 40 public tokens for Alice. Switch the private key back to Bob. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpFo72g7N9iFt3JzzeG8CqsS5doAiXyFvNCgk2oHvjRCzF +" > .env + +leo run transfer_private_to_public "{ + owner: aleo17vy26rpdhqx4598y5gp7nvaa9rk7tnvl6ufhvvf4calsrrqdaqyshdsf5z.private, + amount: 80u64.private, + _nonce: 1852830456042139988098466781381363679605019151318121788109768539956661608520group.public +}" aleo13ssze66adjjkt795z9u5wpq8h6kn0y2657726h4h3e3wfnez4vqsm3008q 40u64 +``` + +When we call `transfer_private_to_public`, we take Bob's private record that contains 110 tokens, and outputs a record owned by Bob with 70 tokens, and calls the finalize function under `transfer_private_to_public` with Alice's address and 40 tokens as arguments. This changes the public mapping under Alice's address to contain 100 public tokens. Again, public mappings are queryable on-chain. diff --git a/documentation/leo/14_battleship.md b/documentation/leo/14_battleship.md new file mode 100644 index 000000000..0e97b991f --- /dev/null +++ b/documentation/leo/14_battleship.md @@ -0,0 +1,872 @@ +--- +id: battleship +title: A battleship game in Leo +--- + +## Contents + +- [Summary](#summary) +- [Build](#how-to-build) +- [Run](#how-to-run) + - [1. Initializing the Players](#1-initializing-the-players) + - [2: Player 1 Places Ships On The Board](#2-player-1-places-ships-on-the-board) + - [3: Player 1 Passes The Board To Player 2](#3-player-1-passes-the-board-to-player-2) + - [4: Player 2 Places Ships On The Board](#4-player-2-places-ships-on-the-board) + - [5: Passing The Board Back To Player 1](#5-passing-the-board-back-to-player-1) + - [6: Player 1 Takes The 1st Turn](#6-player-1-takes-the-1st-turn) + - [7: Player 2 Takes The 2nd Turn](#7-player-2-takes-the-2nd-turn) + - [8: Player 1 Takes The 3rd Turn](#8-player-1-takes-the-3rd-turn) + - [9: Player 2 Takes The 4th Turn](#9-player-2-takes-the-4th-turn) + - [10. Who Wins?](#10-who-wins) +- [ZK Battleship Privacy](#zk-battleship-privacy) +- [Modeling the Boards and Ships](#modeling-the-board-and-ships) +- [Validating a Single Ship](#validating-a-single-ship-at-a-time) +- [Validating all Ships](#validating-all-ships-together-in-a-single-board) +- [Sequencing Game State](#ensure-that-players-and-boards-cannot-swap-mid-game) +- [Preventing Double Moves](#ensure-that-each-player-can-only-move-once-before-the-next-player-can-move) +- [Ensuring Valid Moves](#enforce-constraints-on-valid-moves-and-force-the-player-to-give-their-opponent-information-about-their-opponents-previous-move-in-order-to-continue-playing) +- [Winning](#winning-the-game) + +## Summary + +Battleship is a game where two players lay their ships into secret configurations on their respective 8x8 grids, +and then take turns firing upon each other's board. +The game ends when one player has sunk all of the other player's ships. + +This application was translated into Leo from the [zk-battleship](https://github.com/demox-labs/zk-battleship) example written by the Aleo community - show them some love! + +## How to Run + +Follow the [Leo Installation Instructions](https://developer.aleo.org/leo/installation). + +This battleship program can be run using the following bash script. Locally, it will execute Leo program functions to create the board, place ships, and play a game of battleship. + +```bash +cd battleship +./run.sh +``` + +The `.env` file contains a private key and address. This is the account that will be used to sign transactions and is checked for record ownership. When executing programs as different parties, be sure to set the `private_key` field in `.env` to the appropriate value. You can check out how we've set things up in `./run.sh` for a full example of how to run the program as different parties. + +## 1. Initializing the Players +In order to play battleship, there must be two players with two boards. Players will be represented by their Aleo address. + +We will be playing the role of these two parties: + +```bash +The private key and address of player 1. +private_key: APrivateKey1zkpGKaJY47BXb6knSqmT3JZnBUEGBDFAWz2nMVSsjwYpJmm +address: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy + +The private key and address of player 2. +private_key: APrivateKey1zkp86FNGdKxjgAdgQZ967bqBanjuHkAaoRe19RK24ZCGsHH +address: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry +``` + +## 2. Player 1 Places Ships on the Board +Now, we need to make a board as Player 1. See the [modeling the boards and ships](#modeling-the-board-and-ships) section for information on valid ship bitstrings and placements on the board. + +With player 1's private key, they initialize the board with the placement of 4 ships and the opponent's public address. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpGKaJY47BXb6knSqmT3JZnBUEGBDFAWz2nMVSsjwYpJmm +" > .env + +leo run initialize_board 34084860461056u64 551911718912u64 7u64 1157425104234217472u64 aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry +``` + +```bash +➡️ Output + + • { + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + hits_and_misses: 0u64.private, + played_tiles: 0u64.private, + ships: 1157459741006397447u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + game_started: false.private, + _nonce: 605849623036268790365773177565562473735086364071033205649960161942593750353group.public +} + +Leo ✅ Finished 'battleship.aleo/initialize_board' +``` + +The output is a board_state record owned by Player 1. +Notice that the `game_started` flag is false, as well as the composite ship configuration `ships`. 1157459741006397447u64 to a binary bitstring becomes `0001000000010000000111111000000010000000100000001000000000000111`, +or laid out in columns and rows: +``` +0 0 0 1 0 0 0 0 +0 0 0 1 0 0 0 0 +0 0 0 1 1 1 1 1 +1 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 +0 0 0 0 0 1 1 1 +``` + +## 3: Player 1 Passes The Board To Player 2 +Now, we can offer a battleship game to player 2. Run `offer_battleship` with the record you just created: + +``` +leo run offer_battleship "{ + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + hits_and_misses: 0u64.private, + played_tiles: 0u64.private, + ships: 1157459741006397447u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + game_started: false.private, + _nonce: 605849623036268790365773177565562473735086364071033205649960161942593750353group.public +}" +``` + +```bash +➡️ Outputs + + • { + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + hits_and_misses: 0u64.private, + played_tiles: 0u64.private, + ships: 1157459741006397447u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + game_started: true.private, + _nonce: 5443521912126792569907060514335205174032013684291524549930033539632156136027group.public +} + • { + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + incoming_fire_coordinate: 0u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + prev_hit_or_miss: 0u64.private, + _nonce: 6986401140057557061321899375524513841643724821230599181456639629979203966487group.public +} + +Leo ✅ Finished 'battleship.aleo/offer_battleship' +``` + +The first output record is the updated `board_state.record`. Notice the `game_started` flag is now true. This board cannot be used to offer any other battleship games or accept any battleship game offers. Player 1 would need to initialize a new board and use that instead. The second output record is a dummy `move.record` - there are no fire coordinates included to play on Player 2's board, and no information about any previous Player 2 moves (Player 2 has not made any moves yet). This `move.record` is owned by Player 2, who must use that in combination with their own `board_state.record` to accept the game. Let's do that now. + +## 4: Player 2 Places Ships On The Board + +We switch our .env to player 2's private key and similarly run initialize_board to create a new and different board for player two. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp86FNGdKxjgAdgQZ967bqBanjuHkAaoRe19RK24ZCGsHH +" > .env + +leo run initialize_board 31u64 2207646875648u64 224u64 9042383626829824u64 aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy +``` + +```bash +➡️ Output + + • { + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + hits_and_misses: 0u64.private, + played_tiles: 0u64.private, + ships: 9044591273705727u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + game_started: false.private, + _nonce: 677929557867990662961068737825412945684193990901139603462104629310061710321group.public +} + +✅ Executed 'battleship.aleo/initialize_board' +``` + +Note, the output ships here is 9044591273705727u64, which in a bitstring is: +``` +0 0 1 0 0 0 0 0 +0 0 1 0 0 0 1 0 +0 0 0 0 0 0 1 0 +0 0 0 0 0 0 1 0 +0 0 0 0 0 0 1 0 +0 0 0 0 0 0 0 0 +1 1 1 1 1 1 1 1 +``` + +## 5: Passing The Board Back To Player 1 + +Now, we can accept Player 1's offer. Run `start_battleship`: + +```bash +leo run start_battleship "{ + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + hits_and_misses: 0u64.private, + played_tiles: 0u64.private, + ships: 9044591273705727u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + game_started: false.private, + _nonce: 677929557867990662961068737825412945684193990901139603462104629310061710321group.public +}" "{ + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + incoming_fire_coordinate: 0u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + prev_hit_or_miss: 0u64.private, + _nonce: 6306786918362462465996698473371289503655844751914031374264794338640697795225group.public +}" +``` + +```bash +➡️ Outputs + + • { + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + hits_and_misses: 0u64.private, + played_tiles: 0u64.private, + ships: 9044591273705727u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + game_started: true.private, + _nonce: 499506036017893504519951074816367233238764881167148207158107765834843789278group.public +} + • { + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + incoming_fire_coordinate: 0u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + prev_hit_or_miss: 0u64.private, + _nonce: 7551593771072417773015833444631669906818701068612998340960968556531564726874group.public +} + +✅ Executed 'battleship.aleo/start_battleship' +``` + +Notice the outputs here are similar to `offer_battleship`. A dummy `move.record` is owned by Player 1, and Player 2 gets a `board_state.record` with the `game_started` flag updated. However, now that Player 1 has a `move.record` and a started board, they can begin to play. + +## 6: Player 1 Takes The 1st Turn + +We switch the .env back to player 1, and we run the transition function play. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpGKaJY47BXb6knSqmT3JZnBUEGBDFAWz2nMVSsjwYpJmm +" > .env + +leo run play "{ + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + hits_and_misses: 0u64.private, + played_tiles: 0u64.private, + ships: 1157459741006397447u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + game_started: true.private, + _nonce: 6313341191294792052861773157032837489809107102476040695601777954897783350080group.public +}" "{ + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + incoming_fire_coordinate: 0u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + prev_hit_or_miss: 0u64.private, + _nonce: 2798663115519921626400765401803177719929914180089719334947022448579691220488group.public +}" 1u64 +``` + +```bash +➡️ Outputs + + • { + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + hits_and_misses: 0u64.private, + played_tiles: 1u64.private, + ships: 1157459741006397447u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + game_started: true.private, + _nonce: 5833516448655036599597838063894464861371198938108460526636526325286738488235group.public +} + • { + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + incoming_fire_coordinate: 1u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + prev_hit_or_miss: 0u64.private, + _nonce: 4383078917685812690935470339923943658033179718952229417171392956492546325808group.public +} + +✅ Executed 'battleship.aleo/play' +``` + +Player 1 has an updated `board_state.record` - they have a new `played_tiles` bitstring, which corresponds to the fire coordinate they just sent to Player 2. You can see that the `incoming_fire_coordinate` in the `move.record` owned by Player 2 matches exactly the input given by Player 1. Player 2 can now play this move tile and respond with a fire coordinate of their own, and they will also let Player 1 know whether their fire coordinate hit or miss Player 2's ships. + +## 7: Player 2 Takes The 2nd Turn + +We switch the .env back to player 2, and we run the transition function play. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp86FNGdKxjgAdgQZ967bqBanjuHkAaoRe19RK24ZCGsHH +" > .env + +leo run play "{ + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + hits_and_misses: 0u64.private, + played_tiles: 0u64.private, + ships: 9044591273705727u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + game_started: true.private, + _nonce: 6864275139988909612799168784231775829713739147830284979332684562641318182923group.public +}" "{ + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + incoming_fire_coordinate: 1u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + prev_hit_or_miss: 0u64.private, + _nonce: 8420474443174402614458578667801578345975509805478103542095622903412594983971group.public +}" 2048u64 +``` + +```bash +➡️ Outputs + + • { + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + hits_and_misses: 0u64.private, + played_tiles: 2048u64.private, + ships: 9044591273705727u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + game_started: true.private, + _nonce: 6284479302801058138006361960649628992876976428745392660731784830148359328839group.public +} + • { + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + incoming_fire_coordinate: 2048u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + prev_hit_or_miss: 1u64.private, + _nonce: 8217837260140600949756911248177622179381338760298068527463640818659709985441group.public +} + +✅ Executed 'battleship.aleo/play' +``` + +Player 2 now has an updated `board_state.record` which includes their newly updated `played_tiles`, only containing the fire coordinate they just sent to Player 1. Player 1 now owns a new `move.record` which includes the `hits_and_misses` field. +This contains only the result of Player 1's previous fire coordinate they had sent to Player 2. It will always be a single coordinate on the 8x8 grid if it's a hit. A miss is 0u64 (8x8 grid of 0s), whereas a hit is the u64 equivalent of their previous fire coordinate in bitstring form. + +If you check Player 2's ships configuration, you'll note their entire bottom row is covered by two ships, so sample valid hits on the bottom row would be: 1u64, 2u64, 4u64, 8u64, 16u64, 32u64, 64u64, and 128u64. Since Player 1's first fire coordinate (1u64) was a hit, the `hits_and_misses` field is also 1u64. + +Player 1's next move will consume this `move.record`, which will update Player 1's board with the hit-or-miss, as well as figure out the result of Player 2's fire coordinate. Now that Player 1 has some `played_tiles`, they can no longer choose an alread-played fire coordinate. For example, running `aleo run play 'board_state.record' 'move.record' 1u64` will fail, because 1u64 has already been played. + +## 8: Player 1 Takes The 3rd Turn + +We switch the .env back to player 1, and we run the transition function play. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkpGKaJY47BXb6knSqmT3JZnBUEGBDFAWz2nMVSsjwYpJmm +" > .env + +leo run play "{ + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + hits_and_misses: 0u64.private, + played_tiles: 1u64.private, + ships: 1157459741006397447u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + game_started: true.private, + _nonce: 1962122153746742645258971561783872712461616481157617568489391338473028502271group.public +}" "{ + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + incoming_fire_coordinate: 2048u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + prev_hit_or_miss: 1u64.private, + _nonce: 1204008848449868423802652577996848559012797694551224583683080100053831915439group.public +}" 2u64 +``` + +```bash +➡️ Outputs + + • { + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + hits_and_misses: 1u64.private, + played_tiles: 3u64.private, + ships: 1157459741006397447u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + game_started: true.private, + _nonce: 5338125050531864311985370830280952305688629865354830939402745656578990650505group.public +} + • { + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + incoming_fire_coordinate: 2u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + prev_hit_or_miss: 0u64.private, + _nonce: 7971995563631235472540847437984726419106193784727086463494463811056252801811group.public +} + +✅ Executed 'battleship.aleo/play' +``` + +As before, both a `board_state.record` and `move.record` are created. The `board_state.record` now contains 3u64 as the `played_tiles`, which looks like this in bitstring form: +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 1 1 +``` + +The `board_state.record` `hits_and_misses` field has also been updated with the result of their previous move. The new `move.record` owned by Player 2 now contains information about whether Player 2's previous move was a hit or miss, as well as Player 1's new fire coordinate. + +## 9: Player 2 Takes The 4th Turn + +We switch the .env back to player 2, and we run the transition function play. + +```bash +echo " +NETWORK=testnet3 +PRIVATE_KEY=APrivateKey1zkp86FNGdKxjgAdgQZ967bqBanjuHkAaoRe19RK24ZCGsHH +" > .env + +leo run play "{ + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + hits_and_misses: 0u64.private, + played_tiles: 2048u64.private, + ships: 9044591273705727u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + game_started: true.private, + _nonce: 591128247205636061702123861968396246163831838278146623498909560875485861872group.public +}" "{ + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + incoming_fire_coordinate: 2u64.private, + player_1: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + player_2: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + prev_hit_or_miss: 0u64.private, + _nonce: 4871574741887919250014604645502780786361650856453535231083359604148337116539group.public +}" 4u64 +``` + +```bash +➡️ Outputs + + • { + owner: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + hits_and_misses: 0u64.private, + played_tiles: 2052u64.private, + ships: 9044591273705727u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + game_started: true.private, + _nonce: 4866144015676673398767235148516158177034901439767024502676546368462039477864group.public +} + • { + owner: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + incoming_fire_coordinate: 4u64.private, + player_1: aleo1wyvu96dvv0auq9e4qme54kjuhzglyfcf576h0g3nrrmrmr0505pqd6wnry.private, + player_2: aleo15g9c69urtdhvfml0vjl8px07txmxsy454urhgzk57szmcuttpqgq5cvcdy.private, + prev_hit_or_miss: 2u64.private, + _nonce: 5304512645876453228434639693756897952439730718508628026257897445388710294282group.public +} + +✅ Executed 'battleship.aleo/play' +``` + +## 10. Who Wins? + +Play continues back and forth between Player 1 and Player 2. When one player has a total of 14 flipped bits in their `hits_and_misses` field on their `board_state.record`, they have won the game. + +## ZK Battleship Privacy + +How can we ensure that the ship configurations of each player remains secret, +while being able to trustlessly and fairly play with their opponent? +By taking advantage of selective privacy powered by zero knowledge proofs on Aleo. + +Broadly speaking, we can follow this general strategy: +1. Create mathematical rules for placing the ships on the board, to ensure that neither player can cheat by stacking all their ships in one place, moving them off the board, or laying them across each other. + +2. Ensure that the players and boards that begin a game cannot be swapped out. + +3. Ensure that each player can only move once before the next player can move. + +4. Enforce constraints on valid moves, and force the player to give their opponent information about their opponent's previous move in order to continue playing. + +## Modeling the board and ships + +Most battleship representations in programs use a 64 character string or an array of arrays (8 arrays of 8 elements each) to model the board state. Unfortunately, Aleo instructions don't represent strings well yet, nor can we use for or while loops. Luckily for us, Aleo has the unsigned 64 bit integer type, or u64. To represent every space on a battleship board, from top left to bottom right, we can use each bit in a u64. For example, an empty board would be: +0u64 = +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +``` + +Battleship is played with 4 different ship types - a ship of length 5, length 4, length 3, and length 2. Some versions of battleship have an extra length 3 ship or another extra ship type, however, we will stick to the most basic version for this project. In order to be a valid ship placement, a ship must be placed vertically or horizontally (no diagonals). On a physical board, a ship cannot break across rows or intersect with another ship, but ships are allowed to touch one another. + +Similar to how we represent a board with a u64 bitstring, we can represent a ship horizontally as a bitstring. We "flip" the bits to represent a ship: +| Length | Bitstring | u64 | +| ------ | --------- | --- | +| 5 | 11111 | 31u64| +| 4 | 1111 | 15u64| +| 3 | 111 | 7u64 | +| 2 | 11 | 3u64 | + +We can also represent a ship vertically as a bitstring. To show this, we need 7 "unflipped" bits (zeroes) in between the flipped bits so that the bits are adjacent vertically. +| Length | Bitstring | u64 | +| --- | --- | --- | +| 5 | 1 00000001 00000001 00000001 00000001 | 4311810305u64 | +| 4 | 1 00000001 00000001 00000001 | 16843009u64 | +| 3 | 1 00000001 00000001 | 65793u64 | +| 2 | 1 00000001 | 257u64 | + +With a board model and ship bitstring models, we can now place ships on a board. + +### Examples of valid board configurations: + +17870284429256033024u64 +``` +1 1 1 1 1 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 1 +0 0 0 0 0 0 0 1 +1 1 1 1 0 0 0 1 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 1 1 +0 0 0 0 0 0 0 0 +``` + +16383u64 +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 1 1 1 1 1 1 +1 1 1 1 1 1 1 1 +``` + +2157505700798988545u64 +``` +0 0 0 1 1 1 0 1 +1 1 1 1 0 0 0 1 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 1 +0 0 0 0 0 0 0 1 +0 0 0 0 0 0 0 1 +0 0 0 0 0 0 0 1 +0 0 0 0 0 0 0 1 +``` + +### Examples of invalid board configurations: + +Ships overlapping the bottom ship: +67503903u64 +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 1 0 0 +0 0 0 0 0 1 1 0 +0 0 0 0 0 1 1 1 +0 0 0 1 1 1 1 1 +``` + +Diagonal ships: +9242549787790754436u64 +``` +1 0 0 0 0 0 0 0 +0 1 0 0 0 1 0 0 +0 0 1 0 0 0 1 0 +0 0 0 1 0 0 0 0 +0 0 0 1 1 0 0 0 +0 0 1 0 0 0 0 1 +0 1 0 0 0 0 1 0 +1 0 0 0 0 1 0 0 +``` + +Ships splitting across rows and columns: +1297811850814034450u64 +``` +0 0 0 1 0 0 1 0 +0 0 0 0 0 0 1 0 +1 1 0 0 0 0 0 1 +0 0 0 0 0 0 0 0 +1 0 0 1 0 0 0 1 +0 0 0 1 0 0 0 0 +0 0 0 1 0 0 1 0 +0 0 0 1 0 0 1 0 +``` + +Given these rules, our strategy will be to validate each individual ship bitstring placement on a board, and then, if all the ships are valid, compose all the positions onto a board and validate that the board with all ships are valid. If each individual ship's position is valid, then all the ships together should be valid unless any overlapping occurs. + +## Validating a single ship at a time + +To follow along with the code, all verification of ship bitstrings is done in verify.aleo. We know a ship is valid if all these conditions are met: +If horizontal: +1. The correct number of bits is flipped (a ship of length 5 should not have 6 flipped bits) +2. All the bits are adjacent to each other. +3. The bits do not split a row. + +If vertical: +1. The correct number of bits is flipped. +2. All the bits are adjacent to each other, vertically. This means that each flipped bit should be separated by exactly 7 unflipped bits. +3. The bits do not split a column. + +If a ship is valid vertically or horizontally, then we know the ship is valid. We just need to check for the bit count, the adjacency of those bits, and make sure those bits do not split a row/column. However, we can't loop through the bit string to count bits, or to make sure those bits don't break across columns. We'll need to turn to special bitwise operations and hacks. + +### Bit Counting + +See the "c_bitcount" closure to follow along with the code. 50 years ago, MIT AI Laboratory published HAKMEM, which was a series of tricks and hacks to speed up processing for bitwise operations. https://w3.pppl.gov/~hammett/work/2009/AIM-239-ocr.pdf We turned to HAKMEM 169 for bitcounting inspiration, although we've tweaked our implementation to be (hopefully) easier to understand. Before diving into details, let's build some intuition. + +Let a,b,c,d be either 0 or 1. Given a polynomial 8a + 4b + 2c + d, how do we find the summation of a + b + c + d? If we subtract subsets of this polynomial, we'll be left with the summation. + +Step 1: 8a + 4b + 2c + d +Step 2: -4a - 2b - c +Step 3: -2a - b +Step 4: - a +Step 5: = a + b + c + d + +This polynomial is basically a bitwise representation of a number, so given a 4 bit number, e.g. 1011 or 13u64, we can follow these instructions to get the bit count. Step 2 is just subtracting the starting number but bit shifted to the right (equivalent to dividing by 2). Step 3 bit shifts the starting number to the right twice and is subtracted, and Step 4 bit shifts thrice and is subtracted. Put another way: Start with a 4-digit binary number A. A - (A >> 1) - (A >> 2) - (A >> 3) = B. + +Step 1: 1101 = 13u64 +Step 2: -0110 = 6u64 +Step 3: -0011 = 3u64 +Step 4: -0001 = 1u64 +Step 5: =0011 = 3u64 + +To make this process work for any bit-length number, where the sum of the bits is left in groups of 4 bits, we'll need to use some bit-masking, so that the sum of one group of 4 does not interfere with the next group of 4. +With a larger starting number, like 1111 0001 0111 0110, we will need the following bit maskings: + +``` +For A >> 1, we'll use 0111 0111 0111 .... (in u64, this is 8608480567731124087u64) +For A >> 2, we'll use 0011 0011 0011 .... (in u64, this is 3689348814741910323u64) +For A >> 3, we'll use 0001 0001 0001 .... (in u64, this is 1229782938247303441u64) +``` + +For example, finding the sums of groups of 4 with a 16-bit number we'll call A to yield the bit sum number B: + +``` +A: 1111 0001 0111 0110 +A>>1: 0111 1000 1011 1011 +A>>2: 0011 1100 0101 1101 +A>>3: 0001 1110 0010 1110 + +A>>1: 0111 1000 1011 1011 + & 0111 0111 0111 0111: + 0111 0000 0011 0011 + +A>>2: 0011 1100 0101 1101 + & 0011 0011 0011 0011: + 0011 0000 0001 0001 + +A>>3: 0001 1110 0010 1110 + & 0001 0001 0001 0001: + 0001 0000 0000 0000 + +A - (A>>1 & 0111....) - (A>>2 & 0011....) - (A>>3 & 0001....): +B: 0100 0001 0011 0010 + 4 1 3 2 +``` + +The next step is to combine the summation of each of those 4-bit groups into sums of 8-bit groups. To do this, we'll use another bit trick. We will shift this number B to the right by 4 (B >> 4), and add that back to B. Then, we'll apply a bit masking of 0000 1111 0000 1111 .... (in u64, this is 1085102592571150095u64) to yield the sums of bits in groups of 8, a number we'll call C. + +``` +B: 0100 0001 0011 0010 +B>>4: 0000 0100 0001 0011 + 0100 0101 0100 0101 + 4 5 4 5 + +apply the bit mask + 0000 1111 0000 1111 + +C: 0000 0101 0000 0101 + 0 5 0 5 +``` + +At this point, we've gone from a bit sum in groups of 4 to bit sums in groups of 8. That's great, but ultimately we want the total sum of bits in the original binary number. The final bit trick is to modulo C by 255. This is 2^8 - 1. For a bit of intuition, consider the number 1 0000 0001. If we take 1 0000 0001 mod 256, we're left with 1. If we take 1 0000 0001 mod 255, we're left with 2. Modding by 255 gives us the amount of bits _beyond_ the first 255 numbers, as 255 is the largest number that can be represented with 8 bits. + +A full summary of abbreviated steps to get the bit count, starting with a 64 bit integer A (closely following the c_bitcount closure in the verify.aleo code): + +``` +let A = 64 unsigned bit integer +let B = A - (A>>1 & 8608480567731124087u64) - (A>>2 & 3689348814741910323u64) - (A>>3 & 1229782938247303441u64) +let C = (B - B>>4) & 1085102592571150095u64 +bit count = C mod 255u64 +``` + +### Adjacency Check + +Given a ship's placement on the board and its bitstring representation (horizontally or vertically), we can determine if the bits are adjacent. Follow the c_adjacency_check closure in verify.aleo. Given the ship of length 2, we know it's horizontal bitstring is 11 (3u64) and it's vertical bitstring is 100000001 (257u64). If on the board, the ship starts at the bottom right corner, its horizontal ship placement string would be: +3u64 +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 1 1 +``` + +Vertical ship placement: +257u64 +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 1 +0 0 0 0 0 0 0 1 +``` + +If we move the ship to the left one column: +Horizontal 6u64 +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 1 1 0 +``` + +Vertical 514u64 +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 1 0 +0 0 0 0 0 0 1 0 +``` + +If we move the ship up one row: +Horizontal 768u64 +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 1 1 +0 0 0 0 0 0 0 0 +``` + +Vertical 65792u64 +``` +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 1 +0 0 0 0 0 0 0 1 +0 0 0 0 0 0 0 0 +``` + +We can make the observation that the original bitstring is always shifted by a power of 2 to get to a new valid position on the board. Therefore, if we take the ship placement bitstring and divide by the ship bitstring (either horizontal or vertical), as long as the remaining number is a power of 2 (2^0, 2^1, 2^2, 2^3...), we know the ship's bits are adjacent. + +To ensure that the remaining number is a power of 2, we can use a bit trick. See the bit trick for ensuring a bitstring is a power of 2 section. + +In the code, you'll notice one extra step. Dividing a ship placement bitstring by a ship bitstring representation could result in 0, and then subtracting by 1 will result in an underflow. In that case, we know the ship placement is not valid, so we can set a number which is gauranteed to not be a power of 2. + + +### Splitting a row or column + +Follow the c_horizontal_check closure in verify.aleo to follow the code. Assume all the bits are adjacent (see the adjacency check section). The column case is trivial. We can be certain that if a ship bitstring splits columns, the division of that ship placement bitstring by its ship bitstring representation will not yield a power of 2, and it would have failed the adjacency check. + +The horizontal case must be checked because a split row bitstring could still contain a ship with adjacent bits. To make this check easier, we will condense the 64 bitstring into an 8 bitstring by taking it modulo 255. If we assume that a bitstring is not splitting a row, then taking the ship placement bitstring modulo 255 will yield an 8 bit valid bitstring. If the original ship placement bitstring is not valid, then we will have an invalid 8 bit bitstring. E.g.: + +``` +1 1 1 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +``` +mod 255 = 11100000 (valid) + +``` +0 0 0 0 0 0 0 1 +1 1 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 +``` +mod 255 = 11000001 (invalid) + +How do we know the 8 bit bitstring is valid or not? We can simply do an adjacency check, as before. + +### Ensuring a bitstring is a power of 2 + +Any power of 2 will have a single bit flipped. If we subtract 1 from that number, it will result in a complementary bitstring that, bitwise-anded with the original, will always result in 0. + +E.g. +``` +8: 1000 +8-1: 0111 +8&7: 0000 == 0 + +7: 0111 +7-1: 0110 +7&6: 0110 != 0 +``` + +## Validating all ships together in a single board + +Give individual valid ship position bitstrings, we can combine all these together into a single board using bitwise or operators. See the create_board function in verify.aleo to follow the code. Once all ships are on the board, we can count the total number of bits, which should be 14 exactly for a ship of length 5, 4, 3, and 2. + +## Ensure that players and boards cannot swap mid-game + +Board states are represented with the board_state record. Each board has a flag indicating whether a game has been started with the board. This flag is set when offering a battleship game to an opponent, or accepting a battleship game from an opponent. Move records are created only in 3 ways: +1. Offering a battleship game creates a dummy move record that sets the two players to the addresses set in the board state record. +2. Accepting a battleship game consumes the first dummy move record and checks that the move record contains the same two players as the board of the player accepting the game. Then, a new dummy move record is created and keeps the same two players. +2. A move record must be consumed in order to play and create the next move record. There's a check to ensure the players in the move record matches the players in the board, and the players in the next move record are automatically set. + +The only way moves _not_ matching a board can be combined is if the players begin multiple games with each other. As long as one player is honest and only accepts a single game with a particular opponent, only one set of moves can be played on one board between them. + +## Ensure that each player can only move once before the next player can move + +A move record must be consumed in order to create the next move record. The owner of the move record changes with each play. Player A must spend a move record in order to create a move record containing their fire coordinate, and that move record will be owned by Player B. Player B must spend that move record in order to create the next move record, which will belong to Player A. + +## Enforce constraints on valid moves, and force the player to give their opponent information about their opponent's previous move in order to continue playing + +A valid move for a player is a fire coordinate that has only one flipped bit in a u64. We can make sure only one bit is flipped with the powers of 2 bit trick. That single bit must be a coordinate that has not been played by that player before, which we check in board.aleo/update_played_tiles. + +In order to give their next move to their opponent, a player must call the main.aleo/play function, which checks the opponent's fire coordinate on the current player's board. The move record being created is updated with whether that fire coordinate was a hit or a miss for the opponent. + +## Winning the game + +Right now, the way to check when a game has been won is to count the number of hits on your hits_and_misses field on your board_state record. 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