Implement BN256's G1 functionality.

- Ported over the BN256's G1 functionality from derohe's bh256.go file.
- Updated CurePoint's toString() method: Create a copy of the object to avoid updating the values of the object when calling toString().
- Used UByteArray in GfP's marshal/unmarshal methods to fix issue with negative numbers.
- Fixed an issue with how the carry is calculated in gfpMul method and added a test to confirm its correct behavior.
- Used UByteArray in Lattice's multi method to avoid issues with negative numbers.
- Added a test to confirm that G1 marshal and unmarshal methods work correctly.

library/crypto/src/main/kotlin/net/agorise/library/crypto/bn256/Bn256.kt

@@ -0,0 +1,145 @@
+@file:OptIn(ExperimentalUnsignedTypes::class)
+
+package net.agorise.library.crypto.bn256
+
+import java.math.BigInteger
+import java.security.SecureRandom
+
+/*
+ * Package bn256 implements a particular bilinear group at the 128-bit security
+ * level.
+ *
+ * Bilinear groups are the basis of many of the new cryptographic protocols that
+ * have been proposed over the past decade. They consist of a triplet of groups
+ * (G₁, G₂ and GT) such that there exists a function e(g₁ˣ,g₂ʸ)=gTˣʸ (where gₓ
+ * is a generator of the respective group). That function is called a pairing
+ * function.
+ *
+ * This package specifically implements the Optimal Ate pairing over a 256-bit
+ * Barreto-Naehrig curve as described in
+ * http://cryptojedi.org/papers/dclxvi-20100714.pdf. Its output is not
+ * compatible with the implementation described in that paper, as different
+ * parameters are chosen.
+ *
+ * (This package previously claimed to operate at a 128-bit security level.
+ * However, recent improvements in attacks mean that is no longer true. See
+ * https://moderncrypto.org/mail-archive/curves/2016/000740.html.)
+ *
+ * Ported over from https://github.com/deroproject/derohe/blob/main/cryptography/bn256/bn256.go
+ */
+
+fun randomK(random: SecureRandom): BigInteger {
+    var k: BigInteger
+    do {
+        k = BigInteger(Constants.Order.bitLength(), random).mod(Constants.Order)
+    } while (k.signum() != 1)
+    return k
+}
+
+/*
+ * G1 is an abstract cyclic group. The zero value is suitable for use as the
+ * output of an operation, but cannot be used as an input.
+ */
+class G1(var p: CurvePoint = CurvePoint()) {
+    override fun toString(): String {
+        return "bn256.G1: $p"
+    }
+
+    // ScalarBaseMult sets e to g*k where g is the generator of the group and then returns e.
+    fun scalarBaseMult(k: BigInteger): G1 {
+        this.p.mul(CurvePoint.curveGen, k)
+        return this
+    }
+
+    // ScalarMult sets e to a*k and then returns e.
+    fun scalarMult(a: G1, k: BigInteger): G1 {
+        this.p.mul(a.p, k)
+        return this
+    }
+
+    // Add sets e to a+b and then returns e.
+    fun add(a: G1, b: G1): G1 {
+        this.p.add(a.p, b.p)
+        return this
+    }
+
+    // Neg sets e to -a and then returns e.
+    fun neg(a: G1): G1 {
+        this.p.neg(a.p)
+        return this
+    }
+
+    // Set sets e to a and then returns e.
+    fun set(a: G1): G1 {
+        p.set(a.p)
+        return this
+    }
+
+    // Marshal converts e to a byte slice.
+    fun marshal(): UByteArray {
+        // Each value is a 256-bit number.
+        val numBytes = 256 / 8
+
+        this.p.makeAffine()
+        val ret = UByteArray(numBytes * 2)
+        if (this.p.isInfinity()) {
+            return ret
+        }
+        val temp = GfP()
+
+        montDecode(temp, this.p.x)
+        temp.marshal(ret)
+        montDecode(temp, this.p.y)
+        temp.marshal(ret, numBytes)
+
+        return ret
+    }
+
+    // Unmarshal sets e to the result of converting the output of Marshal back into
+    // a group element and then returns e.
+    fun unmarshal(m: UByteArray): Result<UByteArray> {
+        // Each value is a 256-bit number.
+        val numBytes = 256 / 8
+        if (m.size < 2 * numBytes) {
+            return Result.failure(IllegalArgumentException("bn256: not enough data"))
+        }
+        // Unmarshal the points and check their caps
+        this.p.x = GfP()
+        this.p.y = GfP()
+
+        try {
+            this.p.x.unmarshal(m)
+            this.p.y.unmarshal(m, numBytes)
+        } catch (e: Throwable) {
+            return Result.failure(e)
+        }
+
+        // Encode into Montgomery form and ensure it's on the curve
+        montEncode(this.p.x, this.p.x)
+        montEncode(this.p.y, this.p.y)
+
+        val zero = GfP()
+        if (this.p.x == zero && this.p.y == zero) {
+            // This is the point at infinity.
+            this.p.y = GfP.newGfP(1)
+            this.p.z = GfP()
+            this.p.t = GfP()
+        } else {
+            this.p.z = GfP.newGfP(1)
+            this.p.t = GfP.newGfP(1)
+
+            if (this.p.isOnCurve().not()) {
+                return Result.failure(IllegalArgumentException("bn256: malformed point"))
+            }
+        }
+        return Result.success(m.copyOfRange(2 * numBytes, m.size))
+    }
+
+    companion object {
+        // RandomG1 returns x and g₁ˣ where x is a random, non-zero number read from r.
+        fun randomG1(random: SecureRandom): Pair<BigInteger, G1> {
+            val k = randomK(random)
+            return Pair(k, G1().scalarBaseMult(k))
+        }
+    }
+}

library/crypto/src/main/kotlin/net/agorise/library/crypto/bn256/CurvePoint.kt

@@ -7,20 +7,23 @@ import java.math.BigInteger
  * form and t=z² when valid. G₁ is the set of points of this curve on GF(p).
  * Ported over from https://github.com/deroproject/derohe/blob/main/cryptography/bn256/curve.go
  */
-internal class CurvePoint(
-    private var x: GfP,
-    private var y: GfP,
-    private var z: GfP,
-    private var t: GfP,
+class CurvePoint(
+    var x: GfP,
+    var y: GfP,
+    var z: GfP,
+    var t: GfP,
 ) {
-    private constructor() : this(GfP(0UL), GfP(0UL), GfP(0UL), GfP(0UL))
+    constructor() : this(GfP(), GfP(), GfP(), GfP())
 
     override fun toString(): String {
-        makeAffine()
+        // Create a copy of the object to avoid modifying the original one
+        val copy = CurvePoint(this.x.copy(), this.y.copy(), this.z.copy(), this.t.copy())
+
+        copy.makeAffine()
         val x = GfP()
         val y = GfP()
-        montDecode(x, this.x)
-        montDecode(y, this.y)
+        montDecode(x, copy.x)
+        montDecode(y, copy.y)
         return "($x, $y)"
     }
 
@@ -223,10 +226,10 @@ internal class CurvePoint(
 
         // curveGen is the generator of G₁.
         internal val curveGen = CurvePoint(
-            GfP.newGfP(1),
-            GfP.newGfP(2),
-            GfP.newGfP(1),
-            GfP.newGfP(1),
+            x = GfP.newGfP(1),
+            y = GfP.newGfP(2),
+            z = GfP.newGfP(1),
+            t = GfP.newGfP(1),
         )
     }
 }

library/crypto/src/main/kotlin/net/agorise/library/crypto/bn256/GfP.kt

@@ -18,7 +18,9 @@ class GfP(val data: ULongArray) {
     }
 
     override fun toString(): String {
-        return String.format("%016x %016x %016x %016x", data[3].toLong(), data[2].toLong(), data[1].toLong(), data[0].toLong())
+        // Easier for testing
+        return data.joinToString(separator = " ", transform = { it.toString(10) })
+//        return data.reversed().joinToString(separator = " ", transform = { it.toString(16) })
     }
 
     override fun equals(other: Any?): Boolean {
@@ -54,19 +56,19 @@ class GfP(val data: ULongArray) {
         set(sum)
     }
 
-    fun marshal(out: ByteArray) {
+    fun marshal(out: UByteArray, offset: Int = 0) {
         for (w in 0 until 4) {
             for (b in 0 until 8) {
-                out[8 * w + b] = (data[3 - w] shr (56 - 8 * b)).toByte()
+                out[offset + 8 * w + b] = (data[3 - w] shr (56 - 8 * b)).toUByte()
             }
         }
     }
 
-    fun unmarshal(`in`: ByteArray) {
+    fun unmarshal(`in`: UByteArray, offset: Int = 0) {
         for (w in 0 until 4) {
             data[3 - w] = 0UL
             for (b in 0 until 8) {
-                data[3 - w] += `in`[8 * w + b].toULong() shl (56 - 8 * b)
+                data[3 - w] += `in`[offset + 8 * w + b].toULong() shl (56 - 8 * b)
             }
         }
 

library/crypto/src/main/kotlin/net/agorise/library/crypto/bn256/GfPGeneric.kt

@@ -78,7 +78,7 @@ fun gfpMul(c: GfP, a: GfP, b: GfP) {
         val ti = t[i]
         val zi = Ti + ti + carry
         T[i] = zi
-        carry = (Ti and ti or (Ti or ti) and zi.inv()) shr 63
+        carry = ((Ti and ti) or ((Ti or ti) and zi.inv())) shr 63
     }
 
     c.data[0] = T[4]

library/crypto/src/main/kotlin/net/agorise/library/crypto/bn256/Lattice.kt

@@ -1,3 +1,5 @@
+@file:OptIn(ExperimentalUnsignedTypes::class)
+
 package net.agorise.library.crypto.bn256
 
 import java.math.BigInteger
@@ -52,14 +54,15 @@ internal class Lattice(
         }
     }
 
-    fun multi(scalar: BigInteger): ByteArray {
+    fun multi(scalar: BigInteger): UByteArray {
         val decomp = decompose(scalar)
         val maxLen = decomp.maxOf { it.bitLength() }
 
-        val out = ByteArray(maxLen)
+        val out = UByteArray(maxLen)
         for ((j, x) in decomp.withIndex()) {
             for (i in 0 until maxLen) {
-                out[i] = (out[i] + (if (x.testBit(i)) 1 else 0) shl j).toByte()
+                val bitValue = if (x.testBit(i)) 1u else 0u
+                out[i] = (out[i] + (bitValue shl j)).toUByte()
             }
         }
         return out

library/crypto/src/test/kotlin/net/agorise/library/crypto/bn256/Bn256Test.kt

@@ -0,0 +1,24 @@
+@file:OptIn(ExperimentalUnsignedTypes::class)
+
+package net.agorise.library.crypto.bn256
+
+import java.security.SecureRandom
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class Bn256Test {
+    @Test
+    fun `given a randomly generated G1 - when marshal and unmarshal are called - then result is correct`() {
+        val random = SecureRandom()
+        val (_, ga) = G1.randomG1(random)
+        val ma = ga.marshal()
+
+        val gb = G1()
+        gb.unmarshal(ma)
+
+        val mb = gb.marshal()
+
+        println(ma.toList())
+        assertEquals(ma.toList(), mb.toList(), "bytes are different")
+    }
+}

library/crypto/src/test/kotlin/net/agorise/library/crypto/bn256/GfPTest.kt

@@ -51,4 +51,16 @@ class GfPTest {
 
         assertEquals(expectedGfP.data.toList(), actualGfP.data.toList())
     }
+
+    @Test
+    fun `given two dec GfP values - when gfpMul is called - then result is correct`() {
+        val aGfP = GfP(ulongArrayOf(15230403791020821917UL, 754611498739239741UL, 7381016538464732716UL, 1011752739694698287UL))
+        val bGfP = GfP(ulongArrayOf(4792239181621121553UL, 12809537390334529128UL, 17379557665190828237UL, 110455090769457822UL))
+        val expectedGfP = GfP(ulongArrayOf(4792239181621121553UL, 12809537390334529128UL, 17379557665190828237UL, 110455090769457822UL))
+        val actualGfP = GfP()
+
+        gfpMul(actualGfP, aGfP, bGfP)
+
+        assertEquals(expectedGfP.data.toList(), actualGfP.data.toList())
+    }
 }