[FEAT] pow field Arithmetic API

icicle/include/icicle/fields/complex_extension.h

@@ -210,6 +210,17 @@ class ComplexExtensionField
     FF xs_norm_squared = FF::sqr(xs.real) - nonresidue_times_im;
     return xs_conjugate * ComplexExtensionField{FF::inverse(xs_norm_squared), FF::zero()};
   }
+
+  static constexpr HOST_DEVICE ComplexExtensionField pow(ComplexExtensionField base, int exp)
+  {
+    ComplexExtensionField res = one();
+    while (exp > 0) {
+      if (exp & 1) res = res * base;
+      base = base * base;
+      exp >>= 1;
+    }
+    return res;
+  }
 };
 
 #ifdef __CUDACC__

icicle/include/icicle/fields/quartic_extension.h

@@ -251,6 +251,17 @@ class QuarticExtensionField
       FF::reduce(FF::mul_wide(xs.im1, x2) - FF::mul_wide(xs.im3, x0)),
     };
   }
+
+  static constexpr HOST_DEVICE QuarticExtensionField pow(QuarticExtensionField base, int exp)
+  {
+    QuarticExtensionField res = one();
+    while (exp > 0) {
+      if (exp & 1) res = res * base;
+      base = base * base;
+      exp >>= 1;
+    }
+    return res;
+  }
 };
 #if __CUDACC__
 template <class CONFIG, class T>

icicle/src/fields/ffi_extern.cpp

@@ -28,6 +28,11 @@ extern "C" void CONCAT_EXPAND(FIELD, inv)(scalar_t* scalar1, scalar_t* result)
   *result = scalar_t::inverse(*scalar1);
 }
 
+extern "C" void CONCAT_EXPAND(FIELD, pow)(scalar_t* base, int exp, scalar_t* result)
+{
+  *result = scalar_t::pow(*base, exp);
+}
+
 #ifdef EXT_FIELD
 extern "C" void CONCAT_EXPAND(FIELD, extension_generate_scalars)(extension_t* scalars, int size)
 {
@@ -53,4 +58,9 @@ extern "C" void CONCAT_EXPAND(FIELD, extension_inv)(extension_t* scalar1, extens
 {
   *result = extension_t::inverse(*scalar1);
 }
+
+extern "C" void CONCAT_EXPAND(FIELD, extension_pow)(extension_t* base, int exp, extension_t* result)
+{
+  *result = extension_t::pow(*base, exp);
+}
 #endif // EXT_FIELD

wrappers/golang/curves/bls12377/g2/include/scalar_field.h

@@ -16,6 +16,7 @@ void bls12_377_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_377_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_377_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_377_inv(const scalar_t* a, scalar_t* result);
+void bls12_377_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/bls12377/include/scalar_field.h

@@ -16,6 +16,7 @@ void bls12_377_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_377_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_377_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_377_inv(const scalar_t* a, scalar_t* result);
+void bls12_377_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/bls12377/scalar_field.go

@@ -168,6 +168,18 @@ func (f ScalarField) Sqr() ScalarField {
 	return res
 }
 
+func (f ScalarField) Pow(exp int) ScalarField {
+	var res ScalarField
+
+	cF := (*C.scalar_t)(unsafe.Pointer(&f))
+	cExp := (C.int)(exp)
+	cRes := (*C.scalar_t)(unsafe.Pointer(&res))
+
+	C.bls12_377_pow(cF, cExp, cRes)
+
+	return res
+}
+
 func convertScalarsMontgomery(scalars core.HostOrDeviceSlice, isInto bool) runtime.EIcicleError {
 	defaultCfg := core.DefaultVecOpsConfig()
 	cValues, _, _, cCfg, cSize := core.VecOpCheck(scalars, scalars, scalars, &defaultCfg)

wrappers/golang/curves/bls12377/tests/scalar_field_test.go

@@ -119,6 +119,11 @@ func testScalarFieldArithmetic(suite *suite.Suite) {
 
 	suite.Equal(square, mul, "Square and multiplication do not yield the same value")
 
+	pow4 := scalarA.Pow(4)
+	mulBySelf := mul.Mul(&mul)
+
+	suite.Equal(pow4, mulBySelf, "Square and multiplication do not yield the same value")
+
 	inv := scalarA.Inv()
 
 	one := scalarA.Mul(&inv)

wrappers/golang/curves/bls12381/g2/include/scalar_field.h

@@ -16,6 +16,7 @@ void bls12_381_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_381_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_381_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_381_inv(const scalar_t* a, scalar_t* result);
+void bls12_381_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/bls12381/include/scalar_field.h

@@ -16,6 +16,7 @@ void bls12_381_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_381_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_381_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bls12_381_inv(const scalar_t* a, scalar_t* result);
+void bls12_381_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/bls12381/scalar_field.go

@@ -168,6 +168,18 @@ func (f ScalarField) Sqr() ScalarField {
 	return res
 }
 
+func (f ScalarField) Pow(exp int) ScalarField {
+	var res ScalarField
+
+	cF := (*C.scalar_t)(unsafe.Pointer(&f))
+	cExp := (C.int)(exp)
+	cRes := (*C.scalar_t)(unsafe.Pointer(&res))
+
+	C.bls12_381_pow(cF, cExp, cRes)
+
+	return res
+}
+
 func convertScalarsMontgomery(scalars core.HostOrDeviceSlice, isInto bool) runtime.EIcicleError {
 	defaultCfg := core.DefaultVecOpsConfig()
 	cValues, _, _, cCfg, cSize := core.VecOpCheck(scalars, scalars, scalars, &defaultCfg)

wrappers/golang/curves/bls12381/tests/scalar_field_test.go

@@ -119,6 +119,11 @@ func testScalarFieldArithmetic(suite *suite.Suite) {
 
 	suite.Equal(square, mul, "Square and multiplication do not yield the same value")
 
+	pow4 := scalarA.Pow(4)
+	mulBySelf := mul.Mul(&mul)
+
+	suite.Equal(pow4, mulBySelf, "Square and multiplication do not yield the same value")
+
 	inv := scalarA.Inv()
 
 	one := scalarA.Mul(&inv)

wrappers/golang/curves/bn254/g2/include/scalar_field.h

@@ -16,6 +16,7 @@ void bn254_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bn254_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bn254_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bn254_inv(const scalar_t* a, scalar_t* result);
+void bn254_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/bn254/include/scalar_field.h

@@ -16,6 +16,7 @@ void bn254_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bn254_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bn254_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bn254_inv(const scalar_t* a, scalar_t* result);
+void bn254_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/bn254/scalar_field.go

@@ -168,6 +168,18 @@ func (f ScalarField) Sqr() ScalarField {
 	return res
 }
 
+func (f ScalarField) Pow(exp int) ScalarField {
+	var res ScalarField
+
+	cF := (*C.scalar_t)(unsafe.Pointer(&f))
+	cExp := (C.int)(exp)
+	cRes := (*C.scalar_t)(unsafe.Pointer(&res))
+
+	C.bn254_pow(cF, cExp, cRes)
+
+	return res
+}
+
 func convertScalarsMontgomery(scalars core.HostOrDeviceSlice, isInto bool) runtime.EIcicleError {
 	defaultCfg := core.DefaultVecOpsConfig()
 	cValues, _, _, cCfg, cSize := core.VecOpCheck(scalars, scalars, scalars, &defaultCfg)

wrappers/golang/curves/bn254/tests/scalar_field_test.go

@@ -119,6 +119,11 @@ func testScalarFieldArithmetic(suite *suite.Suite) {
 
 	suite.Equal(square, mul, "Square and multiplication do not yield the same value")
 
+	pow4 := scalarA.Pow(4)
+	mulBySelf := mul.Mul(&mul)
+
+	suite.Equal(pow4, mulBySelf, "Square and multiplication do not yield the same value")
+
 	inv := scalarA.Inv()
 
 	one := scalarA.Mul(&inv)

wrappers/golang/curves/bw6761/g2/include/scalar_field.h

@@ -16,6 +16,7 @@ void bw6_761_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bw6_761_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bw6_761_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bw6_761_inv(const scalar_t* a, scalar_t* result);
+void bw6_761_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/bw6761/include/scalar_field.h

@@ -16,6 +16,7 @@ void bw6_761_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bw6_761_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bw6_761_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void bw6_761_inv(const scalar_t* a, scalar_t* result);
+void bw6_761_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/bw6761/scalar_field.go

@@ -168,6 +168,18 @@ func (f ScalarField) Sqr() ScalarField {
 	return res
 }
 
+func (f ScalarField) Pow(exp int) ScalarField {
+	var res ScalarField
+
+	cF := (*C.scalar_t)(unsafe.Pointer(&f))
+	cExp := (C.int)(exp)
+	cRes := (*C.scalar_t)(unsafe.Pointer(&res))
+
+	C.bw6_761_pow(cF, cExp, cRes)
+
+	return res
+}
+
 func convertScalarsMontgomery(scalars core.HostOrDeviceSlice, isInto bool) runtime.EIcicleError {
 	defaultCfg := core.DefaultVecOpsConfig()
 	cValues, _, _, cCfg, cSize := core.VecOpCheck(scalars, scalars, scalars, &defaultCfg)

wrappers/golang/curves/bw6761/tests/scalar_field_test.go

@@ -119,6 +119,11 @@ func testScalarFieldArithmetic(suite *suite.Suite) {
 
 	suite.Equal(square, mul, "Square and multiplication do not yield the same value")
 
+	pow4 := scalarA.Pow(4)
+	mulBySelf := mul.Mul(&mul)
+
+	suite.Equal(pow4, mulBySelf, "Square and multiplication do not yield the same value")
+
 	inv := scalarA.Inv()
 
 	one := scalarA.Mul(&inv)

wrappers/golang/curves/grumpkin/include/scalar_field.h

@@ -16,6 +16,7 @@ void grumpkin_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void grumpkin_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void grumpkin_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void grumpkin_inv(const scalar_t* a, scalar_t* result);
+void grumpkin_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/curves/grumpkin/scalar_field.go

@@ -168,6 +168,18 @@ func (f ScalarField) Sqr() ScalarField {
 	return res
 }
 
+func (f ScalarField) Pow(exp int) ScalarField {
+	var res ScalarField
+
+	cF := (*C.scalar_t)(unsafe.Pointer(&f))
+	cExp := (C.int)(exp)
+	cRes := (*C.scalar_t)(unsafe.Pointer(&res))
+
+	C.grumpkin_pow(cF, cExp, cRes)
+
+	return res
+}
+
 func convertScalarsMontgomery(scalars core.HostOrDeviceSlice, isInto bool) runtime.EIcicleError {
 	defaultCfg := core.DefaultVecOpsConfig()
 	cValues, _, _, cCfg, cSize := core.VecOpCheck(scalars, scalars, scalars, &defaultCfg)

wrappers/golang/curves/grumpkin/tests/scalar_field_test.go

@@ -119,6 +119,11 @@ func testScalarFieldArithmetic(suite *suite.Suite) {
 
 	suite.Equal(square, mul, "Square and multiplication do not yield the same value")
 
+	pow4 := scalarA.Pow(4)
+	mulBySelf := mul.Mul(&mul)
+
+	suite.Equal(pow4, mulBySelf, "Square and multiplication do not yield the same value")
+
 	inv := scalarA.Inv()
 
 	one := scalarA.Mul(&inv)

wrappers/golang/fields/babybear/extension/extension_field.go

@@ -168,6 +168,18 @@ func (f ExtensionField) Sqr() ExtensionField {
 	return res
 }
 
+func (f ExtensionField) Pow(exp int) ExtensionField {
+	var res ExtensionField
+
+	cF := (*C.scalar_t)(unsafe.Pointer(&f))
+	cExp := (C.int)(exp)
+	cRes := (*C.scalar_t)(unsafe.Pointer(&res))
+
+	C.babybear_extension_pow(cF, cExp, cRes)
+
+	return res
+}
+
 func convertScalarsMontgomery(scalars core.HostOrDeviceSlice, isInto bool) runtime.EIcicleError {
 	defaultCfg := core.DefaultVecOpsConfig()
 	cValues, _, _, cCfg, cSize := core.VecOpCheck(scalars, scalars, scalars, &defaultCfg)

wrappers/golang/fields/babybear/extension/include/scalar_field.h

@@ -16,6 +16,7 @@ void babybear_extension_add(const scalar_t* a, const scalar_t* b, scalar_t* resu
 void babybear_extension_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void babybear_extension_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void babybear_extension_inv(const scalar_t* a, scalar_t* result);
+void babybear_extension_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/fields/babybear/include/scalar_field.h

@@ -16,6 +16,7 @@ void babybear_add(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void babybear_sub(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void babybear_mul(const scalar_t* a, const scalar_t* b, scalar_t* result);
 void babybear_inv(const scalar_t* a, scalar_t* result);
+void babybear_pow(const scalar_t* a, int exp, scalar_t* result);
 
 #ifdef __cplusplus
 }

wrappers/golang/fields/babybear/scalar_field.go

@@ -168,6 +168,18 @@ func (f ScalarField) Sqr() ScalarField {
 	return res
 }
 
+func (f ScalarField) Pow(exp int) ScalarField {
+	var res ScalarField
+
+	cF := (*C.scalar_t)(unsafe.Pointer(&f))
+	cExp := (C.int)(exp)
+	cRes := (*C.scalar_t)(unsafe.Pointer(&res))
+
+	C.babybear_pow(cF, cExp, cRes)
+
+	return res
+}
+
 func convertScalarsMontgomery(scalars core.HostOrDeviceSlice, isInto bool) runtime.EIcicleError {
 	defaultCfg := core.DefaultVecOpsConfig()
 	cValues, _, _, cCfg, cSize := core.VecOpCheck(scalars, scalars, scalars, &defaultCfg)

wrappers/golang/fields/babybear/tests/extension_field_test.go

@@ -119,6 +119,11 @@ func testExtensionFieldArithmetic(suite *suite.Suite) {
 
 	suite.Equal(square, mul, "Square and multiplication do not yield the same value")
 
+	pow4 := scalarA.Pow(4)
+	mulBySelf := mul.Mul(&mul)
+
+	suite.Equal(pow4, mulBySelf, "Square and multiplication do not yield the same value")
+
 	inv := scalarA.Inv()
 
 	one := scalarA.Mul(&inv)

wrappers/golang/fields/babybear/tests/scalar_field_test.go

@@ -119,6 +119,11 @@ func testScalarFieldArithmetic(suite *suite.Suite) {
 
 	suite.Equal(square, mul, "Square and multiplication do not yield the same value")
 
+	pow4 := scalarA.Pow(4)
+	mulBySelf := mul.Mul(&mul)
+
+	suite.Equal(pow4, mulBySelf, "Square and multiplication do not yield the same value")
+
 	inv := scalarA.Inv()
 
 	one := scalarA.Mul(&inv)

wrappers/golang/internal/generator/fields/templates/field.go.tmpl

@@ -171,6 +171,18 @@ func (f {{.FieldPrefix}}Field) Sqr() {{.FieldPrefix}}Field {
 	return res
 }
 
+func (f {{.FieldPrefix}}Field) Pow(exp int) {{.FieldPrefix}}Field {
+	var res {{.FieldPrefix}}Field
+
+	cF := (*C.scalar_t)(unsafe.Pointer(&f))
+	cExp := (C.int)(exp)
+    cRes := (*C.scalar_t)(unsafe.Pointer(&res))
+
+	C.{{.Field}}_pow(cF, cExp, cRes)
+
+	return res
+}
+
 func convertScalarsMontgomery(scalars core.HostOrDeviceSlice, isInto bool) runtime.EIcicleError {
 	defaultCfg := core.DefaultVecOpsConfig()
 	cValues, _, _, cCfg, cSize := core.VecOpCheck(scalars, scalars, scalars, &defaultCfg)

wrappers/golang/internal/generator/fields/templates/field_test.go.tmpl

@@ -120,6 +120,11 @@ func test{{.FieldPrefix}}FieldArithmetic(suite *suite.Suite) {
 
     suite.Equal(square, mul, "Square and multiplication do not yield the same value")
 
+	pow4 := scalarA.Pow(4)
+	mulBySelf := mul.Mul(&mul)
+
+	suite.Equal(pow4, mulBySelf, "Square and multiplication do not yield the same value")
+
     inv := scalarA.Inv()
 
     one := scalarA.Mul(&inv)