package r1csqap import ( "bytes" "math/big" "testing" "github.com/arnaucube/go-snark/fields" "github.com/stretchr/testify/assert" ) func TestTranspose(t *testing.T) { b0 := big.NewInt(int64(0)) b1 := big.NewInt(int64(1)) bFive := big.NewInt(int64(5)) a := [][]*big.Int{ []*big.Int{b0, b1, b0, b0, b0, b0}, []*big.Int{b0, b0, b0, b1, b0, b0}, []*big.Int{b0, b1, b0, b0, b1, b0}, []*big.Int{bFive, b0, b0, b0, b0, b1}, } aT := Transpose(a) assert.Equal(t, aT, [][]*big.Int{ []*big.Int{b0, b0, b0, bFive}, []*big.Int{b1, b0, b1, b0}, []*big.Int{b0, b0, b0, b0}, []*big.Int{b0, b1, b0, b0}, []*big.Int{b0, b0, b1, b0}, []*big.Int{b0, b0, b0, b1}, }) } func neg(a *big.Int) *big.Int { return new(big.Int).Neg(a) } func TestPol(t *testing.T) { b0 := big.NewInt(int64(0)) b1 := big.NewInt(int64(1)) b2 := big.NewInt(int64(2)) b3 := big.NewInt(int64(3)) b4 := big.NewInt(int64(4)) b5 := big.NewInt(int64(5)) b6 := big.NewInt(int64(6)) b16 := big.NewInt(int64(16)) a := []*big.Int{b1, b0, b5} b := []*big.Int{b3, b0, b1} // new Finite Field r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10) assert.True(nil, ok) f := fields.NewFq(r) // new Polynomial Field pf := NewPolynomialField(f) // polynomial multiplication o := pf.Mul(a, b) assert.Equal(t, o, []*big.Int{b3, b0, b16, b0, b5}) // polynomial division quo, rem := pf.Div(a, b) assert.Equal(t, quo[0].Int64(), int64(5)) assert.Equal(t, new(big.Int).Sub(rem[0], r).Int64(), int64(-14)) // check the rem result without modulo c := []*big.Int{neg(b4), b0, neg(b2), b1} d := []*big.Int{neg(b3), b1} quo2, rem2 := pf.Div(c, d) assert.Equal(t, quo2, []*big.Int{b3, b1, b1}) assert.Equal(t, rem2[0].Int64(), int64(5)) // polynomial addition o = pf.Add(a, b) assert.Equal(t, o, []*big.Int{b4, b0, b6}) // polynomial subtraction o1 := pf.Sub(a, b) o2 := pf.Sub(b, a) o = pf.Add(o1, o2) assert.True(t, bytes.Equal(b0.Bytes(), o[0].Bytes())) assert.True(t, bytes.Equal(b0.Bytes(), o[1].Bytes())) assert.True(t, bytes.Equal(b0.Bytes(), o[2].Bytes())) c = []*big.Int{b5, b6, b1} d = []*big.Int{b1, b3} o = pf.Sub(c, d) assert.Equal(t, o, []*big.Int{b4, b3, b1}) // NewPolZeroAt o = pf.NewPolZeroAt(3, 4, b4) assert.Equal(t, pf.Eval(o, big.NewInt(3)), b4) o = pf.NewPolZeroAt(2, 4, b3) assert.Equal(t, pf.Eval(o, big.NewInt(2)), b3) } func TestLagrangeInterpolation(t *testing.T) { // new Finite Field r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10) assert.True(nil, ok) f := fields.NewFq(r) // new Polynomial Field pf := NewPolynomialField(f) b0 := big.NewInt(int64(0)) b5 := big.NewInt(int64(5)) a := []*big.Int{b0, b0, b0, b5} alpha := pf.LagrangeInterpolation(a) assert.Equal(t, pf.Eval(alpha, big.NewInt(int64(4))), b5) aux := pf.Eval(alpha, big.NewInt(int64(3))).Int64() assert.Equal(t, aux, int64(0)) } func TestR1CSToQAP(t *testing.T) { // new Finite Field r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10) assert.True(nil, ok) f := fields.NewFq(r) // new Polynomial Field pf := NewPolynomialField(f) b0 := big.NewInt(int64(0)) b1 := big.NewInt(int64(1)) b3 := big.NewInt(int64(3)) b5 := big.NewInt(int64(5)) b9 := big.NewInt(int64(9)) b27 := big.NewInt(int64(27)) b30 := big.NewInt(int64(30)) b35 := big.NewInt(int64(35)) a := [][]*big.Int{ []*big.Int{b0, b1, b0, b0, b0, b0}, []*big.Int{b0, b0, b0, b1, b0, b0}, []*big.Int{b0, b1, b0, b0, b1, b0}, []*big.Int{b5, b0, b0, b0, b0, b1}, } b := [][]*big.Int{ []*big.Int{b0, b1, b0, b0, b0, b0}, []*big.Int{b0, b1, b0, b0, b0, b0}, []*big.Int{b1, b0, b0, b0, b0, b0}, []*big.Int{b1, b0, b0, b0, b0, b0}, } c := [][]*big.Int{ []*big.Int{b0, b0, b0, b1, b0, b0}, []*big.Int{b0, b0, b0, b0, b1, b0}, []*big.Int{b0, b0, b0, b0, b0, b1}, []*big.Int{b0, b0, b1, b0, b0, b0}, } alphas, betas, gammas, zx := pf.R1CSToQAP(a, b, c) // fmt.Println(alphas) // fmt.Println(betas) // fmt.Println(gammas) // fmt.Print("Z(x): ") // fmt.Println(zx) w := []*big.Int{b1, b3, b35, b9, b27, b30} ax, bx, cx, px := pf.CombinePolynomials(w, alphas, betas, gammas) // fmt.Println(ax) // fmt.Println(bx) // fmt.Println(cx) // fmt.Println(px) hx := pf.DivisorPolynomial(px, zx) // fmt.Println(hx) // hx==px/zx so px==hx*zx assert.Equal(t, px, pf.Mul(hx, zx)) // p(x) = a(x) * b(x) - c(x) == h(x) * z(x) abc := pf.Sub(pf.Mul(ax, bx), cx) assert.Equal(t, abc, px) hz := pf.Mul(hx, zx) assert.Equal(t, abc, hz) }