implement multiplication for polyval

circuits/aes-gcm/gfmul.circom

@@ -0,0 +1,231 @@
+pragma circom 2.1.9;
+
+include "mul.circom";
+
+// Computes carryless POLYVAL multiplication over GF(2^128) in constant time.
+//
+// Method described at:
+// <https://www.bearssl.org/constanttime.html#ghash-for-gcm>
+//
+// POLYVAL multiplication is effectively the little endian equivalent of
+// GHASH multiplication, aside from one small detail described here:
+//
+// <https://crypto.stackexchange.com/questions/66448/how-does-bearssls-gcm-modular-reduction-work/66462#66462>
+//
+// > The product of two bit-reversed 128-bit polynomials yields the
+// > bit-reversed result over 255 bits, not 256. The BearSSL code ends up
+// > with a 256-bit result in zw[], and that value is shifted by one bit,
+// > because of that reversed convention issue. Thus, the code must
+// > include a shifting step to put it back where it should
+//
+// This shift is unnecessary for POLYVAL and has been removed.
+//
+// ref: https://github.com/RustCrypto/universal-hashes/blob/master/polyval/src/backend/soft64.rs#L151
+template MUL() {
+    signal input a[2][64];
+    signal input b[2][64];
+    signal output out[2][64];
+
+    // variable aliases to make indexing logic easier to state
+    signal h[3][64];
+    signal y[3][64];
+    signal h_r[3][64];
+    signal y_r[3][64];
+
+    h[0] <== a[0];
+    h[1] <== a[1];
+    y[0] <== b[0];
+    y[1] <== b[1];
+    component Revs[4];
+    for (var i = 0; i < 2; i++) {
+        Revs[i] = REV64();
+        Revs[i].in <== h[i];
+        h_r[i] <== Revs[i].out;
+    }
+    for (var i = 0; i < 2; i++) {
+        Revs[i+2] = REV64();
+        Revs[i+2].in <== y[i];
+        y_r[i] <== Revs[i+2].out;
+    }
+
+    // h2 = h0^h1; y2 = y0^y1
+    component Xors[4];
+    for (var i = 0; i < 4; i++) Xors[i] = BitwiseXor(64);
+    Xors[0].a <== h[0];
+    Xors[0].b <== h[1];
+    h[2] <== Xors[0].out;
+    Xors[1].a <== y[0];
+    Xors[1].b <== y[1];
+    y[2] <== Xors[1].out;
+
+    // h2_r = h0_r^h1_r; y2_r = y0_r^y1_r
+    Xors[2].a <== h_r[0];
+    Xors[2].b <== h_r[1];
+    h_r[2] <== Xors[2].out;
+    Xors[3].a <== y_r[0];
+    Xors[3].b <== y_r[1];
+    y_r[2] <== Xors[3].out;
+
+    // z0 = bmul64(y0, h0); z1 = bmul64(y1, h1); z2 = bmul64(y2, h2);
+    // z0_h = bmul64(y0_r, h0_r); z1_h = bmul64(y1_r, h1_r); z2_h = bmul64(y2_r, h2_r);
+    component BMUL64_z[6];
+    signal z[3][64];
+    signal zh[3][64];
+    for (var i = 0; i < 3; i++) {
+        BMUL64_z[i] = BMUL64();
+        BMUL64_z[i].x <== y[i];
+        BMUL64_z[i].y <== h[i];
+        z[i] <== BMUL64_z[i].out;
+
+        BMUL64_z[i+3] = BMUL64();
+        BMUL64_z[i+3].x <== y_r[i];
+        BMUL64_z[i+3].y <== h_r[i];
+        zh[i] <== BMUL64_z[i+3].out;
+    }
+
+    // _z2 = z0 ^ z1 ^ z2;
+    // _z2h = z0h ^ z1h ^ z2h;
+    signal _z2[64];
+    signal _zh[3][64];
+    component XorMultiples[2];
+    XorMultiples[0] = XorMultiple(3, 64);
+    XorMultiples[0].inputs <== z;
+    _z2 <== XorMultiples[0].out;
+
+    XorMultiples[1] = XorMultiple(3, 64);
+    XorMultiples[1].inputs <== zh;
+    _zh[0] <== XorMultiples[1].out;
+    _zh[1] <== zh[1];
+    _zh[2] <== zh[2];
+
+    // z0h = rev64(z0h) >> 1;
+    // z1h = rev64(z1h) >> 1;
+    // _z2h = rev64(_z2h) >> 1;
+    // signal _zh[3][64];
+    signal __zh[3][64];
+    component Revs_zh[3];
+    component RightShifts_zh[3];
+    for (var i = 0; i < 3; i++) {
+        Revs_zh[i] = REV64();
+        RightShifts_zh[i] = BitwiseRightShift(64, 1);
+        Revs_zh[i].in <== zh[i];
+        RightShifts_zh[i].in <== Revs_zh[i].out;
+        __zh[i] <== RightShifts_zh[i].out;
+    }
+
+    // let v0 = z0;
+    // let mut v1 = z0h ^ z2;
+    // let mut v2 = z1 ^ z2h;
+    // let mut v3 = z1h;
+    signal v[4][64];
+    component Xors_v[2];
+    v[0] <== z[0];
+    v[3] <== __zh[1];
+    Xors_v[0] = BitwiseXor(64);
+    Xors_v[0].a <== __zh[0];
+    Xors_v[0].b <== _z2;
+    v[1] <== Xors_v[0].out;
+    Xors_v[1] = BitwiseXor(64);
+    Xors_v[1].a <== z[1];
+    Xors_v[1].b <== __zh[2];
+    v[2] <== Xors_v[1].out;
+
+
+    // _v2 = v2 ^ v0 ^ (v0 >> 1) ^ (v0 >> 2) ^ (v0 >> 7);
+    // _v1 = v1 ^ (v0 << 63) ^ (v0 << 62) ^ (v0 << 57);
+    // _v3 = v3 ^ _v1 ^ (_v1 >> 1) ^ (_v1 >> 2) ^ (_v1 >> 7);
+    // __v2 = _v2 ^ (_v1 << 63) ^ (_v1 << 62) ^ (_v1 << 57);
+    signal _v2[64];
+    signal _v1[64];
+    signal _v3[64];
+    signal __v2[64];
+    component XorMultiples_v[4];
+    component LeftShifts_v[6];
+    component RightShifts_v[6];
+
+    out <== [__v2, _v3];
+
+}
+
+// Multiplication in GF(2)[X], truncated to the low 64-bits, with “holes”
+// (sequences of zeroes) to avoid carry spilling.
+//
+// When carries do occur, they wind up in a "hole" and are subsequently masked
+// out of the result.
+//
+// ref: https://github.com/RustCrypto/universal-hashes/blob/master/polyval/src/backend/soft64.rs#L206
+template BMUL64() {
+    signal input x[64];
+    signal input y[64];
+    signal output out[64];
+
+    signal xs[4][64];
+    signal ys[4][64];
+    // var masks[4] = [0x1111111111111111, 0x2222222222222222, 0x4444444444444444, 0x8888888888888888];
+    var masks[4][64] = [
+        [0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,
+         0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1],
+        [0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,
+         0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0],
+        [0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,
+         0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0],
+        [1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,
+         1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0]];
+
+    component ands[3][4];
+    for (var i = 0; i < 4; i++) {
+        ands[0][i] = BitwiseAnd(64);
+        ands[0][i].a <== masks[i];
+        ands[0][i].b <== x;
+        xs[i] <== ands[0][i].out;
+
+        ands[1][i] = BitwiseAnd(64);
+        ands[1][i].a <== masks[i];
+        ands[1][i].b <== y;
+        ys[i] <== ands[1][i].out;
+    }
+
+    // w_{i,j} = x_j * y_{i-j%4}
+    component muls[4][4];
+    // z_i = XOR(w_{i,0}, w_{i,1}, w_{i,2}, w_{i,3})
+    component xor_multiples[4];
+    signal z_mid[4][4][64];
+    signal z[4][64];
+    for (var i = 0; i < 4; i++) {
+        for (var j = 0; j < 4; j++) {
+            var Y_INDEX = (i - j) % 4;
+            muls[i][j] = Mul64();
+            muls[i][j].src1 <== xs[j];
+            muls[i][j].src2 <== ys[Y_INDEX];
+            z_mid[i][j] <== muls[i][j].out;
+        }
+
+        xor_multiples[i] = XorMultiple(4, 64);
+        xor_multiples[i].inputs <== z_mid[i];
+        z[i] <== xor_multiples[i].out;
+    }
+
+    // z_masked[i] = z[i] & masks[i]
+    signal z_masked[4][64];
+    for (var i = 0; i < 4; i++) {
+        ands[2][i] = BitwiseAnd(64);
+        ands[2][i].a <== masks[i];
+        ands[2][i].b <== z[i];
+        z_masked[i] <== ands[2][i].out;
+    }
+
+    // out = z_masked[0] | z_masked[1] | z_masked[2] | z_masked[3]
+    component or_multiple = OrMultiple(4, 64);
+    or_multiple.inputs <== z_masked;
+    out <== or_multiple.out;
+}
+
+// todo: verify this is what was actually meant
+template REV64(){
+    signal input in[64];
+    signal output out[64];
+
+    for (var i = 0; i < 64; i++) {
+        out[i] <== in[63 - i];
+    }
+}

circuits/aes-gcm/hashes.circom

@@ -88,11 +88,10 @@ template GHASH(n_msg_bits) {
 // }
 
 
-template POLYVAL(n_msg_bits)
-{
+template POLYVAL(n_msg_bits) {
     signal input msg[n_msg_bits]; 
+    // Hash Key
     signal input H[128]; 
-    // signal input T[2][64]; // TODO
     signal output out[128];
 
     for (var i = 0; i < 128; i++) {

circuits/aes-gcm/helper_functions.circom

@@ -117,6 +117,16 @@ template BitwiseAnd(n) {
     }
 }
 
+template BitwiseOr(n) {
+    signal input a[n];
+    signal input b[n];
+    signal output out[n];
+
+    for (var i=0; i<n; i++) {
+        out[i] <== a[i] + b[i] - a[i]*b[i];
+    }
+}
+
 template IntAnd(n)
 {
     signal input a;
@@ -229,6 +239,47 @@ template SumMultiple(n) {
     sum <== sums[n-1];
 }
 
+// compute the OR of n inputs, each m bits wide
+template OrMultiple(n, m) {
+    signal input inputs[n][m];
+    signal output out[m];
+
+    signal mids[n][m];
+    mids[0] <== inputs[0];
+
+    component ors[n-1];
+    for(var i=0; i<n-1; i++) {
+        ors[i] = BitwiseOr(m);
+        ors[i].a <== mids[i];
+        ors[i].b <== inputs[i+1];
+        mids[i+1] <== ors[i].out;
+    }
+
+    out <== mids[n-1];
+}
+
+// compute the XOR of n inputs, each m bits wide
+template XorMultiple(n, m) {
+    signal input inputs[n][m];
+    signal output out[m];
+
+    signal mids[n][m];
+    mids[0] <== inputs[0];
+
+    component xors[n-1];
+    for(var i=0; i<n-1; i++) {
+        xors[i] = BitwiseXor(m);
+        xors[i].a <== mids[i];
+        xors[i].b <== inputs[i+1];
+        mids[i+1] <== xors[i].out;
+    }
+
+    out <== mids[n-1];
+}
+
+// select the index-th element from an array of total elements
+// via the argument:
+// Sum_0^n (IsEqual(index, i) * in[i])
 template IndexSelector(total) {
     signal input in[total];
     signal input index;
@@ -249,6 +300,7 @@ template IndexSelector(total) {
     out <== calcTotal.sum;
 }
 
+// reverse the bit order in an n-bit array
 template ReverseBitsArray(n) {
     signal input in[n];
     signal output out[n];

circuits/aes-gcm/mul.circom

@@ -2,6 +2,14 @@ pragma circom 2.1.9;
 
 include "helper_functions.circom";
 
+template Mul64()
+{
+    signal input src1[64];
+    signal input src2[64];
+    signal output out[64];
+
+}
+
 template Mul()
 {
     signal input src1[64];

circuits/test/gfmul.test.ts

@@ -0,0 +1,53 @@
+import { assert } from "chai";
+import { WitnessTester } from "circomkit";
+import { bitArrayToHex, circomkit, hexToBitArray } from "./common";
+
+const X = hexToBitArray("0x0100000000000000");
+const Y = hexToBitArray("0x0100000000000000");
+const EXPECT = "";
+
+describe("BMUL64", () => {
+  let circuit: WitnessTester<["x", "y"], ["out"]>;
+
+  before(async () => {
+    circuit = await circomkit.WitnessTester(`BMUL64`, {
+      file: "aes-gcm/gfmul",
+      template: "BMUL64",
+      // params: [8],
+    });
+  });
+
+  // let bit_array = [1,0,0,0,0,0,0,0];
+  // let expected_output = [0,0,0,0,0,0,0,1].map((x) => BigInt(x));
+  it("bmul64", async () => {
+    const _res = await circuit.compute({ x: X, y: Y }, ["out"]);
+    // const result = bitArrayToHex(
+    //   (_res.out as number[]).map((bit) => Number(bit))
+    // ).slice(0, 32);
+    // console.log("expect: ", EXPECT, "\nresult: ", result);
+    // assert.equal(result, EXPECT);
+  });
+});
+
+describe("MUL", () => {
+  let circuit: WitnessTester<["h", "rhs"], ["out"]>;
+
+  before(async () => {
+    circuit = await circomkit.WitnessTester(`MUL64`, {
+      file: "aes-gcm/gfmul",
+      template: "MUL",
+      // params: [8],
+    });
+  });
+
+  // let bit_array = [1,0,0,0,0,0,0,0];
+  // let expected_output = [0,0,0,0,0,0,0,1].map((x) => BigInt(x));
+  it("mul", async () => {
+    const _res = await circuit.compute({ h: X, rhs: Y }, ["out"]);
+    // const result = bitArrayToHex(
+    //   (_res.out as number[]).map((bit) => Number(bit))
+    // ).slice(0, 32);
+    // console.log("expect: ", EXPECT, "\nresult: ", result);
+    // assert.equal(result, EXPECT);
+  });
+});