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Separate int group into IntGroupContext, IntElementModP, IntElementModQ. Move some random methods to Utils.
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,70 @@ | ||
| package org.cryptobiotic.eg.core | ||
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| import org.cryptobiotic.eg.core.Base16.toHex | ||
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| interface Element { | ||
| /** The [GroupContext] it belongs to */ | ||
| val group: GroupContext | ||
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| /** Validates that this element is a member of the Group */ | ||
| fun isValidElement(): Boolean | ||
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| /** Converts to a [ByteArray] representation. Inverse to group.binaryToElementModX(). */ | ||
| fun byteArray(): ByteArray | ||
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| fun toHex() : String = byteArray().toHex() | ||
| } | ||
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| interface ElementModQ : Element, Comparable<ElementModQ> { | ||
| /** Modular addition */ | ||
| operator fun plus(other: ElementModQ): ElementModQ | ||
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| /** Modular subtraction */ | ||
| operator fun minus(other: ElementModQ): ElementModQ | ||
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| /** Modular multiplication */ | ||
| operator fun times(other: ElementModQ): ElementModQ | ||
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| /** Computes the additive inverse */ | ||
| operator fun unaryMinus(): ElementModQ | ||
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| /** Finds the multiplicative inverse */ | ||
| fun multInv(): ElementModQ | ||
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| /** Multiplies by the modular inverse of [denominator] */ | ||
| infix operator fun div(denominator: ElementModQ): ElementModQ | ||
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| /** Allows elements to be compared (<, >, <=, etc.) using the usual arithmetic operators. */ | ||
| override operator fun compareTo(other: ElementModQ): Int | ||
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| /** Checks whether this element is zero. */ | ||
| fun isZero(): Boolean | ||
| } | ||
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| interface ElementModP : Element, Comparable<ElementModP> { | ||
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| /** Computes b^e mod p */ | ||
| infix fun powP(exp: ElementModQ): ElementModP | ||
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| /** Modular multiplication */ | ||
| operator fun times(other: ElementModP): ElementModP | ||
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| /** Finds the multiplicative inverse */ | ||
| fun multInv(): ElementModP | ||
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| /** Multiplies by the modular inverse of [denominator] */ | ||
| infix operator fun div(denominator: ElementModP): ElementModP | ||
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| /** Allows elements to be compared (<, >, <=, etc.) using the usual arithmetic operators. */ | ||
| override operator fun compareTo(other: ElementModP): Int | ||
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| /** Create a new instance of this element where the `powP` function will possibly run faster. */ | ||
| fun acceleratePow(): ElementModP | ||
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| /** Short version of the String for readability. */ | ||
| fun toStringShort(): String { | ||
| val s = toHex() | ||
| val len = s.length | ||
| return "${s.substring(0, 7)}...${s.substring(len-8, len)}" | ||
| } | ||
| } |
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1 change: 0 additions & 1 deletion
1
src/main/kotlin/org/cryptobiotic/eg/core/ecgroup/EcGroupContext.kt
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124 changes: 124 additions & 0 deletions
124
src/main/kotlin/org/cryptobiotic/eg/core/intgroup/IntElementModP.kt
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,124 @@ | ||
| package org.cryptobiotic.eg.core.intgroup | ||
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| import org.cryptobiotic.eg.core.* | ||
| import org.cryptobiotic.eg.core.Base64.toBase64 | ||
| import java.math.BigInteger | ||
| import java.util.concurrent.atomic.AtomicInteger | ||
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| open class IntElementModP(internal val element: BigInteger, val groupContext: IntGroupContext): ElementModP, | ||
| Element, Comparable<ElementModP> { | ||
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| override fun byteArray(): ByteArray = element.toByteArray().normalize(512) | ||
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| private fun BigInteger.modWrap(): ElementModP = this.mod(groupContext.p).wrap() | ||
| private fun BigInteger.wrap(): ElementModP = IntElementModP(this, groupContext) | ||
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| override val group: GroupContext | ||
| get() = groupContext | ||
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| override operator fun compareTo(other: ElementModP): Int = element.compareTo(other.getCompat(groupContext)) | ||
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| /** | ||
| * Validates that this element is in Z_p^r, "set of r-th-residues in Z_p". | ||
| * "A value x is in Z_p^r if and only if x is an integer such that 0 ≤ x < p | ||
| * and x^q mod p == 1", see spec 2.0 p.9. | ||
| */ | ||
| override fun isValidElement(): Boolean { | ||
| groupContext.opCounts.getOrPut("exp") { AtomicInteger(0) }.incrementAndGet() | ||
| val inBounds = this.element >= BigInteger.ZERO && this.element < groupContext.p | ||
| val residue = this.element.modPow(groupContext.q, groupContext.p) == groupContext.oneModP.element | ||
| return inBounds && residue | ||
| } | ||
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| override infix fun powP(exp: ElementModQ) : ElementModP { | ||
| groupContext.opCounts.getOrPut("exp") { AtomicInteger(0) }.incrementAndGet() | ||
| return this.element.modPow(exp.getCompat(groupContext), groupContext.p).wrap() | ||
| } | ||
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| override operator fun times(other: ElementModP) = | ||
| (this.element * other.getCompat(groupContext)).modWrap() | ||
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| override fun multInv() | ||
| = element.modInverse(groupContext.p).wrap() | ||
| // = this powP groupContext.qMinus1Q | ||
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| // Performance note: multInv() can be expressed with the modInverse() method or we can do | ||
| // this exponentiation thing with Q - 1, which works for the subgroup. On the JVM, we get | ||
| // basically the same performance either way. | ||
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| override infix operator fun div(denominator: ElementModP) = | ||
| (element * denominator.getCompat(groupContext).modInverse(groupContext.p)).modWrap() | ||
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| override fun acceleratePow() : ElementModP = | ||
| AcceleratedElementModP(this) | ||
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| fun toMontgomeryElementModP(): MontgomeryElementModP = | ||
| ProductionMontgomeryElementModP( | ||
| element.shiftLeft(groupContext.productionMode.numBitsInP).mod(groupContext.p), | ||
| groupContext | ||
| ) | ||
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| override fun equals(other: Any?) = when (other) { | ||
| is ElementModP -> byteArray().contentEquals(other.byteArray()) | ||
| else -> false | ||
| } | ||
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| override fun hashCode() = byteArray().contentHashCode() | ||
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| override fun toString() = byteArray().toBase64() | ||
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| private fun ElementModP.getCompat(other: IntGroupContext): BigInteger { | ||
| group.assertCompatible(other) | ||
| return when (this) { | ||
| is IntElementModP -> this.element | ||
| else -> throw NotImplementedError("should only be two kinds of elements") | ||
| } | ||
| } | ||
| } | ||
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| class AcceleratedElementModP(p: IntElementModP) : IntElementModP(p.element, p.groupContext) { | ||
| // Laziness to delay computation of the table until its first use; saves space | ||
| val powRadix by lazy { PowRadix(p, p.groupContext.powRadixOption) } | ||
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| override fun acceleratePow(): ElementModP = this | ||
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| override infix fun powP(exp: ElementModQ) : ElementModP { | ||
| groupContext.opCounts.getOrPut("acc") { AtomicInteger(0) }.incrementAndGet() | ||
| return powRadix.pow(exp) | ||
| } | ||
| } | ||
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| internal data class ProductionMontgomeryElementModP(val element: BigInteger, val groupContext: IntGroupContext): | ||
| MontgomeryElementModP { | ||
| internal fun MontgomeryElementModP.getCompat(other: GroupContext): BigInteger { | ||
| context.assertCompatible(other) | ||
| if (this is ProductionMontgomeryElementModP) { | ||
| return this.element | ||
| } else { | ||
| throw NotImplementedError("unexpected MontgomeryElementModP type") | ||
| } | ||
| } | ||
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| internal fun BigInteger.modI(): BigInteger = this and groupContext.montgomeryIMinusOne | ||
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| internal fun BigInteger.divI(): BigInteger = this shr groupContext.productionMode.numBitsInP | ||
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| override fun times(other: MontgomeryElementModP): MontgomeryElementModP { | ||
| // w = aI * bI = (ab)(I^2) | ||
| val w: BigInteger = this.element * other.getCompat(this.context) | ||
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| // Z = ((((W mod I)⋅p^' ) mod I)⋅p+W)/I | ||
| val z: BigInteger = (((w.modI() * groupContext.montgomeryPPrime).modI() * groupContext.p) + w).divI() | ||
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| return ProductionMontgomeryElementModP( | ||
| if (z >= groupContext.p) z - groupContext.p else z, | ||
| groupContext) | ||
| } | ||
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| override fun toElementModP(): ElementModP = | ||
| IntElementModP((element * groupContext.montgomeryIPrime).mod(groupContext.p), groupContext) | ||
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| override val context: GroupContext | ||
| get() = groupContext | ||
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| } |
60 changes: 60 additions & 0 deletions
60
src/main/kotlin/org/cryptobiotic/eg/core/intgroup/IntElementModQ.kt
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,60 @@ | ||
| package org.cryptobiotic.eg.core.intgroup | ||
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| import org.cryptobiotic.eg.core.Base64.toBase64 | ||
| import org.cryptobiotic.eg.core.Element | ||
| import org.cryptobiotic.eg.core.ElementModQ | ||
| import org.cryptobiotic.eg.core.assertCompatible | ||
| import org.cryptobiotic.eg.core.normalize | ||
| import java.math.BigInteger | ||
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| class IntElementModQ(internal val element: BigInteger, override val group: IntGroupContext): ElementModQ, | ||
| Element, Comparable<ElementModQ> { | ||
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| override fun byteArray(): ByteArray = element.toByteArray().normalize(32) | ||
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| private fun BigInteger.modWrap(): ElementModQ = this.mod(this@IntElementModQ.group.q).wrap() | ||
| private fun BigInteger.wrap(): ElementModQ = IntElementModQ(this, this@IntElementModQ.group) | ||
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| override fun isZero() = element == BigInteger.ZERO | ||
| override fun isValidElement() = element >= BigInteger.ZERO && element < this.group.q | ||
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| override operator fun compareTo(other: ElementModQ): Int = element.compareTo(other.getCompat(this.group)) | ||
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| override operator fun plus(other: ElementModQ) = | ||
| (this.element + other.getCompat(this.group)).modWrap() | ||
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| override operator fun minus(other: ElementModQ) = | ||
| this + (-other) | ||
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| override operator fun times(other: ElementModQ) = | ||
| (this.element * other.getCompat(this.group)).modWrap() | ||
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| override fun multInv(): ElementModQ = element.modInverse(this.group.q).wrap() | ||
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| override operator fun unaryMinus(): ElementModQ = | ||
| if (this == this.group.zeroModQ) | ||
| this | ||
| else | ||
| (this.group.q - element).wrap() | ||
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| override infix operator fun div(denominator: ElementModQ): ElementModQ = | ||
| this * denominator.multInv() | ||
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| override fun equals(other: Any?) = when (other) { | ||
| is ElementModQ -> byteArray().contentEquals(other.byteArray()) | ||
| else -> false | ||
| } | ||
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| override fun hashCode() = byteArray().contentHashCode() | ||
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| override fun toString() = byteArray().toBase64() | ||
| } | ||
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| internal fun ElementModQ.getCompat(other: IntGroupContext): BigInteger { | ||
| group.assertCompatible(other) | ||
| return when (this) { | ||
| is IntElementModQ -> this.element | ||
| else -> throw NotImplementedError("should only be two kinds of elements") | ||
| } | ||
| } |
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