Implemented Lattice functionality.
- Ported over Lattice functionality from the derohe project. - Ported over LatticeTest too, to verify that Lattice implementation is correct.
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package net.agorise.library.crypto.bn256
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import java.math.BigInteger
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val half: BigInteger = Constants.Order.shiftRight(1)
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internal val curveLattice = Lattice(
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vectors = arrayOf(
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arrayOf(BigInteger("147946756881789319000765030803803410728"), BigInteger("147946756881789319010696353538189108491")),
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arrayOf(BigInteger("147946756881789319020627676272574806254"), BigInteger("-147946756881789318990833708069417712965"))
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),
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inverse = arrayOf(
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BigInteger("147946756881789318990833708069417712965"),
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BigInteger("147946756881789319010696353538189108491")
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),
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det = BigInteger("43776485743678550444492811490514550177096728800832068687396408373151616991234")
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)
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internal val targetLattice = Lattice(
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vectors = arrayOf(
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arrayOf(BigInteger("9931322734385697761"), BigInteger("9931322734385697761"), BigInteger("9931322734385697763"), BigInteger("9931322734385697764")),
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arrayOf(BigInteger("4965661367192848881"), BigInteger("4965661367192848881"), BigInteger("4965661367192848882"), BigInteger("-9931322734385697762")),
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arrayOf(BigInteger("-9931322734385697762"), BigInteger("-4965661367192848881"), BigInteger("4965661367192848881"), BigInteger("-4965661367192848882")),
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arrayOf(BigInteger("9931322734385697763"), BigInteger("-4965661367192848881"), BigInteger("-4965661367192848881"), BigInteger("-4965661367192848881"))
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),
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inverse = arrayOf(
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BigInteger("734653495049373973658254490726798021314063399421879442165"),
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BigInteger("147946756881789319000765030803803410728"),
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BigInteger("-147946756881789319005730692170996259609"),
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BigInteger("1469306990098747947464455738335385361643788813749140841702")
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),
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det = Constants.Order
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)
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/**
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* Lattice implementation ported over from https://github.com/deroproject/derohe/blob/main/cryptography/bn256/lattice.go
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*/
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class Lattice(val vectors: Array<Array<BigInteger>>, val inverse: Array<BigInteger>, val det: BigInteger) {
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/**
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* takes a scalar mod Order as input and finds a short, positive decomposition of it
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* wrt to the lattice basis.
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*/
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fun decompose(k: BigInteger): Array<BigInteger> {
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val n = inverse.size
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// Calculate closest vector in lattice to <k,0,0,...> with Babai's rounding.
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val c = Array(n) { i ->
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val ci = k.multiply(inverse[i])
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round(ci, det)
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}
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// Transform vectors according to c and subtract <k,0,0,...>.
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val out = Array(n) { BigInteger.ZERO }
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for (i in 0 until n) {
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for (j in 0 until n) {
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val temp = c[j].multiply(vectors[j][i])
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out[i] = out[i].add(temp)
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}
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out[i] = out[i].negate().add(vectors[0][i]).add(vectors[0][i])
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}
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out[0] = out[0].add(k)
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return out
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}
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fun precompute(add: (UInt, UInt) -> Unit) {
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val n = vectors.size
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val total = 1u shl n
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for (i in 0 until n) {
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for (j in 0u until total) {
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if (j shr i and 1u == 1u) {
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add(i.toUInt(), j)
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}
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}
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}
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}
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fun multi(scalar: BigInteger): ByteArray {
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val decomp = decompose(scalar)
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val maxLen = decomp.maxOf { it.bitLength() }
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val out = ByteArray(maxLen)
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for ((j, x) in decomp.withIndex()) {
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for (i in 0 until maxLen) {
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out[i] = (out[i] + (if (x.testBit(i)) 1 else 0) shl j).toByte()
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}
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}
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return out
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}
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/**
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* Returns num/denom rounded to the nearest integer.
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*/
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private fun round(num: BigInteger, denom: BigInteger): BigInteger {
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val remainder = num.remainder(denom)
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val quotient = num.divide(denom)
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return if (remainder > half) {
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quotient.add(BigInteger.ONE)
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} else {
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quotient
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}
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}
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}
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@ -0,0 +1,34 @@
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package net.agorise.library.crypto.bn256
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import java.math.BigInteger
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import java.security.SecureRandom
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import kotlin.test.Test
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import kotlin.test.fail
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class LatticeTest {
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@Test
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fun `given a random number - when decompose is called on curveLattice - then reduction is small`() {
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val random = SecureRandom()
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val k = BigInteger(Constants.Order.bitLength(), random)
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val ks = curveLattice.decompose(k)
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if (ks[0].bitLength() > 130 || ks[1].bitLength() > 130) {
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fail("reduction too large")
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} else if (ks[0].signum() < 0 || ks[1].signum() < 0) {
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fail("reduction must be positive")
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}
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}
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@Test
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fun `given a random number - when decompose is called on targetLattice - then reduction is small`() {
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val random = SecureRandom()
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val k = BigInteger(Constants.Order.bitLength(), random)
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val ks = targetLattice.decompose(k)
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if (ks.any { it.bitLength() > 66 }) {
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fail("reduction too large")
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} else if (ks.any { it.signum() < 0 }) {
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fail("reduction must be positive")
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}
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}
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}
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