implemented optimized poseidon (#38)

* implemented optimized poseidon

* added comment to poseidon hash function

* deleted poseidonslow

poseidon/poseidon.go

@@ -1,7 +1,6 @@
 package poseidon
 
 import (
-	"errors"
 	"fmt"
 	"math/big"
 
@@ -17,6 +16,19 @@ func zero() *ff.Element {
 	return ff.NewElement()
 }
 
+// exp5 performs x^5 mod p
+// https://eprint.iacr.org/2019/458.pdf page 8
+func exp5(a *ff.Element) {
+	a.Exp(*a, 5)
+}
+
+// exp5state perform exp5 for whole state
+func exp5state(state []*ff.Element) {
+	for i := 0; i < len(state); i++ {
+		exp5(state[i])
+	}
+}
+
 // ark computes Add-Round Key, from the paper https://eprint.iacr.org/2019/458.pdf
 func ark(state []*ff.Element, c []*ff.Element, it int) {
 	for i := 0; i < len(state); i++ {
@@ -24,33 +36,21 @@ func ark(state []*ff.Element, c []*ff.Element, it int) {
 	}
 }
 
-// exp5 performs x^5 mod p
-// https://eprint.iacr.org/2019/458.pdf page 8
-func exp5(a *ff.Element) {
-	a.Exp(*a, 5)
-}
-
-// sbox https://eprint.iacr.org/2019/458.pdf page 6
-func sbox(nRoundsF, nRoundsP int, state []*ff.Element, i int) {
-	if (i < nRoundsF/2) || (i >= nRoundsF/2+nRoundsP) {
-		for j := 0; j < len(state); j++ {
-			exp5(state[j])
-		}
-	} else {
-		exp5(state[0])
-	}
-}
-
 // mix returns [[matrix]] * [vector]
-func mix(state []*ff.Element, newState []*ff.Element, m [][]*ff.Element) {
+func mix(state []*ff.Element, t int, m [][]*ff.Element) []*ff.Element {
 	mul := zero()
+	newState := make([]*ff.Element, t)
+	for i := 0; i < t; i++ {
+		newState[i] = zero()
+	}
 	for i := 0; i < len(state); i++ {
 		newState[i].SetUint64(0)
 		for j := 0; j < len(state); j++ {
-			mul.Mul(m[i][j], state[j])
+			mul.Mul(m[j][i], state[j])
 			newState[i].Add(newState[i], mul)
 		}
 	}
+	return newState
 }
 
 // Hash computes the Poseidon hash for the given inputs
@@ -59,29 +59,56 @@ func Hash(inpBI []*big.Int) (*big.Int, error) {
 	if len(inpBI) == 0 || len(inpBI) >= len(NROUNDSP)-1 {
 		return nil, fmt.Errorf("invalid inputs length %d, max %d", len(inpBI), len(NROUNDSP)-1)
 	}
-	if !utils.CheckBigIntArrayInField(inpBI[:]) {
-		return nil, errors.New("inputs values not inside Finite Field")
-	}
 	inp := utils.BigIntArrayToElementArray(inpBI[:])
+
+	nRoundsF := NROUNDSF
+	nRoundsP := NROUNDSP[t-2]
+	C := c.c[t-2]
+	S := c.s[t-2]
+	M := c.m[t-2]
+	P := c.p[t-2]
+
 	state := make([]*ff.Element, t)
 	state[0] = zero()
 	copy(state[1:], inp[:])
 
-	nRoundsF := NROUNDSF
+	ark(state, C, 0)
-	nRoundsP := NROUNDSP[t-2]
 
-	newState := make([]*ff.Element, t)
+	for i := 0; i < nRoundsF/2-1; i++ {
-	for i := 0; i < t; i++ {
+		exp5state(state)
-		newState[i] = zero()
+		ark(state, C, (i+1)*t)
+		state = mix(state, t, M)
+	}
+	exp5state(state)
+	ark(state, C, (nRoundsF/2)*t)
+	state = mix(state, t, P)
+
+	for i := 0; i < nRoundsP; i++ {
+		exp5(state[0])
+		state[0].Add(state[0], C[(nRoundsF/2+1)*t+i])
+
+		mul := zero()
+		newState0 := zero()
+		for j := 0; j < len(state); j++ {
+			mul.Mul(S[(t*2-1)*i+j], state[j])
+			newState0.Add(newState0, mul)
+		}
+
+		for k := 1; k < t; k++ {
+			mul = zero()
+			state[k] = state[k].Add(state[k], mul.Mul(state[0], S[(t*2-1)*i+t+k-1]))
+		}
+		state[0] = newState0
 	}
 
-	// ARK --> SBox --> M, https://eprint.iacr.org/2019/458.pdf pag.5
+	for i := 0; i < nRoundsF/2-1; i++ {
-	for i := 0; i < nRoundsF+nRoundsP; i++ {
+		exp5state(state)
-		ark(state, c.c[t-2], i*t)
+		ark(state, C, (nRoundsF/2+1)*t+nRoundsP+i*t)
-		sbox(nRoundsF, nRoundsP, state, i)
+		state = mix(state, t, M)
-		mix(state, newState, c.m[t-2])
-		state, newState = newState, state
 	}
+	exp5state(state)
+	state = mix(state, t, M)
+
 	rE := state[0]
 	r := big.NewInt(0)
 	rE.ToBigIntRegular(r)