1package plonky2_verifier
 2
 3import (
 4	"fmt"
 5	. "gnark-ed25519/field"
 6
 7	"github.com/consensys/gnark/frontend"
 8)
 9
10type QuadraticExtensionAPI struct {
11	field frontend.API
12
13	W        F
14	DTH_ROOT F
15	ZERO_F   F
16
17	ONE     QuadraticExtension
18	ZERO_QE QuadraticExtension
19}
20
21func NewQuadraticExtensionAPI(field frontend.API, degreeBits uint64) *QuadraticExtensionAPI {
22	// TODO:  Should degreeBits be verified that it fits within the field and that degree is within uint64?
23
24	return &QuadraticExtensionAPI{
25		field: field,
26
27		W:        NewFieldElement(7),
28		DTH_ROOT: NewFieldElement(18446744069414584320),
29		ZERO_F:   NewFieldElement(0),
30
31		ONE:     QuadraticExtension{NewFieldElement(1), NewFieldElement(0)},
32		ZERO_QE: QuadraticExtension{NewFieldElement(0), NewFieldElement(0)},
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.field.Add(c.field.Mul(a[0], b[0]).(F), c.field.Mul(c.W, a[1], b[1])).(F)
42	c_1 := c.field.Add(c.field.Mul(a[0], b[1]).(F), c.field.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.field.Add(a[0], b[0]).(F)
48	c_1 := c.field.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.field.Sub(a[0], b[0]).(F)
54	c_1 := c.field.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.field.IsZero(a[0])
67	a1_is_zero := c.field.IsZero(a[1])
68
69	// assert that a0_is_zero OR a1_is_zero == false
70	c.field.AssertIsEqual(c.field.Mul(a0_is_zero, a1_is_zero).(F), c.ZERO_F)
71
72	a_pow_r_minus_1 := QuadraticExtension{a[0], c.field.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.field.Inverse(a_pow_r[0]).(F))
75}
76
77func (c *QuadraticExtensionAPI) ScalarMulExtension(a QuadraticExtension, scalar F) QuadraticExtension {
78	return QuadraticExtension{c.field.Mul(a[0], scalar).(F), c.field.Mul(a[1], scalar).(F)}
79}
80
81func (c *QuadraticExtensionAPI) FieldToQE(a F) QuadraticExtension {
82	return QuadraticExtension{a, c.ZERO_F}
83}
84
85func (c *QuadraticExtensionAPI) Println(a QuadraticExtension) {
86	fmt.Print("Degree 0 coefficient")
87	c.field.Println(a[0])
88
89	fmt.Print("Degree 1 coefficient")
90	c.field.Println(a[1])
91}