1package plonky2_verifier
  2
  3import (
  4	"fmt"
  5	"gnark-ed25519/field"
  6	. "gnark-ed25519/field"
  7	"math/bits"
  8
  9	"github.com/consensys/gnark/frontend"
 10)
 11
 12type QuadraticExtensionAPI struct {
 13	fieldAPI frontend.API
 14
 15	W        F
 16	DTH_ROOT F
 17
 18	ONE     QuadraticExtension
 19	ZERO_QE QuadraticExtension
 20}
 21
 22func NewQuadraticExtensionAPI(fieldAPI frontend.API, degreeBits uint64) *QuadraticExtensionAPI {
 23	// TODO:  Should degreeBits be verified that it fits within the field and that degree is within uint64?
 24
 25	return &QuadraticExtensionAPI{
 26		fieldAPI: fieldAPI,
 27
 28		W:        NewFieldElement(7),
 29		DTH_ROOT: NewFieldElement(18446744069414584320),
 30
 31		ONE:     QuadraticExtension{ONE_F, ZERO_F},
 32		ZERO_QE: QuadraticExtension{ZERO_F, ZERO_F},
 33	}
 34}
 35
 36func (c *QuadraticExtensionAPI) SquareExtension(a QuadraticExtension) QuadraticExtension {
 37	return c.MulExtension(a, a)
 38}
 39
 40func (c *QuadraticExtensionAPI) MulExtension(a QuadraticExtension, b QuadraticExtension) QuadraticExtension {
 41	c_0 := c.fieldAPI.Add(c.fieldAPI.Mul(a[0], b[0]).(F), c.fieldAPI.Mul(c.W, a[1], b[1])).(F)
 42	c_1 := c.fieldAPI.Add(c.fieldAPI.Mul(a[0], b[1]).(F), c.fieldAPI.Mul(a[1], b[0])).(F)
 43	return QuadraticExtension{c_0, c_1}
 44}
 45
 46func (c *QuadraticExtensionAPI) AddExtension(a QuadraticExtension, b QuadraticExtension) QuadraticExtension {
 47	c_0 := c.fieldAPI.Add(a[0], b[0]).(F)
 48	c_1 := c.fieldAPI.Add(a[1], b[1]).(F)
 49	return QuadraticExtension{c_0, c_1}
 50}
 51
 52func (c *QuadraticExtensionAPI) SubExtension(a QuadraticExtension, b QuadraticExtension) QuadraticExtension {
 53	c_0 := c.fieldAPI.Sub(a[0], b[0]).(F)
 54	c_1 := c.fieldAPI.Sub(a[1], b[1]).(F)
 55	return QuadraticExtension{c_0, c_1}
 56}
 57
 58func (c *QuadraticExtensionAPI) DivExtension(a QuadraticExtension, b QuadraticExtension) QuadraticExtension {
 59	return c.MulExtension(a, c.InverseExtension(b))
 60}
 61
 62// TODO: Instead of calculating the inverse within the circuit, can witness the
 63// inverse and assert that a_inverse * a = 1.  Should reduce # of constraints.
 64func (c *QuadraticExtensionAPI) InverseExtension(a QuadraticExtension) QuadraticExtension {
 65	// First assert that a doesn't have 0 value coefficients
 66	a0_is_zero := c.fieldAPI.IsZero(a[0])
 67	a1_is_zero := c.fieldAPI.IsZero(a[1])
 68
 69	// assert that a0_is_zero OR a1_is_zero == false
 70	c.fieldAPI.AssertIsEqual(c.fieldAPI.Mul(a0_is_zero, a1_is_zero).(F), field.ZERO_F)
 71
 72	a_pow_r_minus_1 := QuadraticExtension{a[0], c.fieldAPI.Mul(a[1], c.DTH_ROOT).(F)}
 73	a_pow_r := c.MulExtension(a_pow_r_minus_1, a)
 74	return c.ScalarMulExtension(a_pow_r_minus_1, c.fieldAPI.Inverse(a_pow_r[0]).(F))
 75}
 76
 77func (c *QuadraticExtensionAPI) ScalarMulExtension(a QuadraticExtension, scalar F) QuadraticExtension {
 78	return QuadraticExtension{c.fieldAPI.Mul(a[0], scalar).(F), c.fieldAPI.Mul(a[1], scalar).(F)}
 79}
 80
 81func (c *QuadraticExtensionAPI) FieldToQE(a F) QuadraticExtension {
 82	return QuadraticExtension{a, field.ZERO_F}
 83}
 84
 85// / Exponentiate `base` to the power of a known `exponent`.
 86func (c *QuadraticExtensionAPI) ExpU64Extension(a QuadraticExtension, exponent uint64) QuadraticExtension {
 87	switch exponent {
 88	case 0:
 89		return c.ONE
 90	case 1:
 91		return a
 92	case 2:
 93		return c.SquareExtension(a)
 94	default:
 95	}
 96
 97	current := a
 98	product := c.ONE
 99
100	for i := 0; i < bits.Len64(exponent); i++ {
101		if i != 0 {
102			current = c.SquareExtension(current)
103		}
104
105		if (exponent >> i & 1) != 0 {
106			product = c.MulExtension(product, current)
107		}
108	}
109
110	return product
111}
112
113func (c *QuadraticExtensionAPI) Println(a QuadraticExtension) {
114	fmt.Print("Degree 0 coefficient")
115	c.fieldAPI.Println(a[0])
116
117	fmt.Print("Degree 1 coefficient")
118	c.fieldAPI.Println(a[1])
119}