multiplication extension gate (#11)

field/field.go

@@ -13,6 +13,8 @@ type QuadraticExtension = [2]F
 type QEAlgebra = [2]QuadraticExtension
 type Hash = [4]F
 
+const D = 2
+
 var TEST_CURVE = ecc.BN254
 
 func NewFieldElement(x uint64) F {

field/quadratic_extension.go

@@ -177,21 +177,21 @@ func (c *QuadraticExtensionAPI) Println(a QuadraticExtension) {
 }
 
 func (c *QuadraticExtensionAPI) MulExtensionAlgebra(a, b QEAlgebra) QEAlgebra {
-	var inner [2][][2]QuadraticExtension
-	var inner_w [2][][2]QuadraticExtension
-	for i := 0; i < 2; i++ {
-		for j := 0; j < 2-i; j++ {
-			idx := (i + j) % 2
+	var inner [D][][2]QuadraticExtension
+	var inner_w [D][][2]QuadraticExtension
+	for i := 0; i < D; i++ {
+		for j := 0; j < D-i; j++ {
+			idx := (i + j) % D
 			inner[idx] = append(inner[idx], [2]QuadraticExtension{a[i], b[j]})
 		}
-		for j := 2 - i; j < 2; j++ {
-			idx := (i + j) % 2
+		for j := D - i; j < D; j++ {
+			idx := (i + j) % D
 			inner_w[idx] = append(inner_w[idx], [2]QuadraticExtension{a[i], b[j]})
 		}
 	}
 
 	var product QEAlgebra
-	for i := 0; i < 2; i++ {
+	for i := 0; i < D; i++ {
 		acc := c.InnerProductExtension(NewFieldElement(7), c.ZERO_QE, inner_w[i])
 		product[i] = c.InnerProductExtension(ONE_F, acc, inner[i])
 	}
@@ -201,7 +201,7 @@ func (c *QuadraticExtensionAPI) MulExtensionAlgebra(a, b QEAlgebra) QEAlgebra {
 
 func (c *QuadraticExtensionAPI) ScalarMulExtensionAlgebra(a QuadraticExtension, b QEAlgebra) QEAlgebra {
 	var product QEAlgebra
-	for i := 0; i < 2; i++ {
+	for i := 0; i < D; i++ {
 		product[i] = c.MulExtension(a, b[i])
 	}
 
@@ -210,7 +210,7 @@ func (c *QuadraticExtensionAPI) ScalarMulExtensionAlgebra(a QuadraticExtension,
 
 func (c *QuadraticExtensionAPI) AddExtensionAlgebra(a, b QEAlgebra) QEAlgebra {
 	var sum QEAlgebra
-	for i := 0; i < 2; i++ {
+	for i := 0; i < D; i++ {
 		sum[i] = c.AddExtension(a[i], b[i])
 	}
 
@@ -219,7 +219,7 @@ func (c *QuadraticExtensionAPI) AddExtensionAlgebra(a, b QEAlgebra) QEAlgebra {
 
 func (c *QuadraticExtensionAPI) SubExtensionAlgebra(a, b QEAlgebra) QEAlgebra {
 	var diff QEAlgebra
-	for i := 0; i < 2; i++ {
+	for i := 0; i < D; i++ {
 		diff[i] = c.SubExtension(a[i], b[i])
 	}
 

plonky2_verifier/arithmetic_extension_gate.go

@@ -5,9 +5,6 @@ import (
 	. "gnark-plonky2-verifier/field"
 )
 
-// Ideally, this should be serialized in the plonky2 repo
-const d = 2
-
 type ArithmeticExtensionGate struct {
 	numOps uint64
 }
@@ -23,19 +20,19 @@ func (g *ArithmeticExtensionGate) Id() string {
 }
 
 func (g *ArithmeticExtensionGate) wiresIthMultiplicand0(i uint64) Range {
-	return Range{4 * d * i, 4*d*i + d}
+	return Range{4 * D * i, 4*D*i + D}
 }
 
 func (g *ArithmeticExtensionGate) wiresIthMultiplicand1(i uint64) Range {
-	return Range{4*d*i + d, 4*d*i + 2*d}
+	return Range{4*D*i + D, 4*D*i + 2*D}
 }
 
 func (g *ArithmeticExtensionGate) wiresIthAddend(i uint64) Range {
-	return Range{4*d*i + 2*d, 4*d*i + 3*d}
+	return Range{4*D*i + 2*D, 4*D*i + 3*D}
 }
 
 func (g *ArithmeticExtensionGate) wiresIthOutput(i uint64) Range {
-	return Range{4*d*i + 3*d, 4*d*i + 4*d}
+	return Range{4*D*i + 3*D, 4*D*i + 4*D}
 }
 
 func (g *ArithmeticExtensionGate) EvalUnfiltered(p *PlonkChip, vars EvaluationVars) []QuadraticExtension {

plonky2_verifier/gate.go

@@ -104,6 +104,24 @@ func GateInstanceFromId(gateId string) gate {
 		return NewArithmeticExtensionGate(uint64(numOps))
 	}
 
+	if strings.HasPrefix(gateId, "MultiplicationExtension") {
+		// Has the format "ArithmeticExtensionGate { num_ops: 10 }"
+
+		regEx := "MultiplicationExtension { num_ops: (?P<numOps>[0-9]+) }"
+		r, err := regexp.Compile(regEx)
+		if err != nil {
+			panic("Invalid MultiplicationExtension regular expression")
+		}
+
+		matches := getRegExMatches(r, gateId)
+		numOps, hasNumOps := matches["numOps"]
+		if !hasNumOps {
+			panic("Invalid MultiplicationExtension ID")
+		}
+
+		return NewMultiplicationExtensionGate(uint64(numOps))
+	}
+
 	return nil
 	//panic(fmt.Sprintf("Unknown gate ID %s", gateId))
 }

plonky2_verifier/gate_test.go

@@ -768,6 +768,7 @@ func TestGates(t *testing.T) {
 		{&RandomAccessGate{bits: 4, numCopies: 4, numExtraConstants: 2}, randomAccessGateExpectedConstraints},
 		{&PoseidonGate{}, poseidonGateExpectedConstraints},
 		{&ArithmeticExtensionGate{numOps: 10}, arithmeticExtensionGateExpectedConstraints},
+		{&MultiplicationExtensionGate{numOps: 13}, mulExtensionGateExpectedConstraints},
 	}
 
 	for _, test := range gateTests {

plonky2_verifier/multiplication_extension_gate.go

@@ -0,0 +1,51 @@
+package plonky2_verifier
+
+import (
+	"fmt"
+	. "gnark-plonky2-verifier/field"
+)
+
+type MultiplicationExtensionGate struct {
+	numOps uint64
+}
+
+func NewMultiplicationExtensionGate(numOps uint64) *MultiplicationExtensionGate {
+	return &MultiplicationExtensionGate{
+		numOps: numOps,
+	}
+}
+
+func (g *MultiplicationExtensionGate) Id() string {
+	return fmt.Sprintf("ArithmeticExtensionGate { num_ops: %d }", g.numOps)
+}
+
+func (g *MultiplicationExtensionGate) wiresIthMultiplicand0(i uint64) Range {
+	return Range{3 * D * i, 3*D*i + D}
+}
+
+func (g *MultiplicationExtensionGate) wiresIthMultiplicand1(i uint64) Range {
+	return Range{3*D*i + D, 3*D*i + 2*D}
+}
+
+func (g *MultiplicationExtensionGate) wiresIthOutput(i uint64) Range {
+	return Range{3*D*i + 2*D, 3*D*i + 3*D}
+}
+
+func (g *MultiplicationExtensionGate) EvalUnfiltered(p *PlonkChip, vars EvaluationVars) []QuadraticExtension {
+	const0 := vars.localConstants[0]
+
+	constraints := []QuadraticExtension{}
+	for i := uint64(0); i < g.numOps; i++ {
+		multiplicand0 := vars.GetLocalExtAlgebra(g.wiresIthMultiplicand0(i))
+		multiplicand1 := vars.GetLocalExtAlgebra(g.wiresIthMultiplicand1(i))
+		output := vars.GetLocalExtAlgebra(g.wiresIthOutput(i))
+
+		mul := p.qeAPI.MulExtensionAlgebra(multiplicand0, multiplicand1)
+		computed_output := p.qeAPI.ScalarMulExtensionAlgebra(const0, mul)
+
+		diff := p.qeAPI.SubExtensionAlgebra(output, computed_output)
+		constraints = append(constraints, diff[0], diff[1])
+	}
+
+	return constraints
+}