testudo/src/unipoly.rs
src/unipoly.rsRaw
1use crate::poseidon_transcript::{AppendToPoseidon, PoseidonTranscript};
2
3use super::commitments::{Commitments, MultiCommitGens};
4use super::group::GroupElement;
5use super::scalar::Scalar;
6use super::transcript::{AppendToTranscript, ProofTranscript};
7use ark_ff::Field;
8use ark_serialize::*;
9use merlin::Transcript;
10// ax^2 + bx + c stored as vec![c,b,a]
11// ax^3 + bx^2 + cx + d stored as vec![d,c,b,a]
12#[derive(Debug, CanonicalDeserialize, CanonicalSerialize, Clone)]
13pub struct UniPoly {
14 pub coeffs: Vec<Scalar>,
15 // pub coeffs_fq: Vec<Fq>,
16}
17
18// ax^2 + bx + c stored as vec![c,a]
19// ax^3 + bx^2 + cx + d stored as vec![d,b,a]
20#[derive(CanonicalSerialize, CanonicalDeserialize, Debug)]
21pub struct CompressedUniPoly {
22 pub coeffs_except_linear_term: Vec<Scalar>,
23}
24
25impl UniPoly {
26 pub fn from_evals(evals: &[Scalar]) -> Self {
27 // we only support degree-2 or degree-3 univariate polynomials
28 assert!(evals.len() == 3 || evals.len() == 4);
29 let coeffs = if evals.len() == 3 {
30 // ax^2 + bx + c
31 let two_inv = Scalar::from(2).inverse().unwrap();
32
33 let c = evals[0];
34 let a = two_inv * (evals[2] - evals[1] - evals[1] + c);
35 let b = evals[1] - c - a;
36 vec![c, b, a]
37 } else {
38 // ax^3 + bx^2 + cx + d
39 let two_inv = Scalar::from(2).inverse().unwrap();
40 let six_inv = Scalar::from(6).inverse().unwrap();
41
42 let d = evals[0];
43 let a = six_inv
44 * (evals[3] - evals[2] - evals[2] - evals[2] + evals[1] + evals[1] + evals[1] - evals[0]);
45 let b = two_inv
46 * (evals[0] + evals[0] - evals[1] - evals[1] - evals[1] - evals[1] - evals[1]
47 + evals[2]
48 + evals[2]
49 + evals[2]
50 + evals[2]
51 - evals[3]);
52 let c = evals[1] - d - a - b;
53 vec![d, c, b, a]
54 };
55
56 UniPoly { coeffs }
57 }
58
59 pub fn degree(&self) -> usize {
60 self.coeffs.len() - 1
61 }
62
63 pub fn as_vec(&self) -> Vec<Scalar> {
64 self.coeffs.clone()
65 }
66
67 pub fn eval_at_zero(&self) -> Scalar {
68 self.coeffs[0]
69 }
70
71 pub fn eval_at_one(&self) -> Scalar {
72 (0..self.coeffs.len()).map(|i| self.coeffs[i]).sum()
73 }
74
75 pub fn evaluate(&self, r: &Scalar) -> Scalar {
76 let mut eval = self.coeffs[0];
77 let mut power = *r;
78 for i in 1..self.coeffs.len() {
79 eval += power * self.coeffs[i];
80 power *= r;
81 }
82 eval
83 }
84
85 pub fn compress(&self) -> CompressedUniPoly {
86 let coeffs_except_linear_term = [&self.coeffs[..1], &self.coeffs[2..]].concat();
87 assert_eq!(coeffs_except_linear_term.len() + 1, self.coeffs.len());
88 CompressedUniPoly {
89 coeffs_except_linear_term,
90 }
91 }
92
93 pub fn commit(&self, gens: &MultiCommitGens, blind: &Scalar) -> GroupElement {
94 self.coeffs.commit(blind, gens)
95 }
96}
97
98impl CompressedUniPoly {
99 // we require eval(0) + eval(1) = hint, so we can solve for the linear term as:
100 // linear_term = hint - 2 * constant_term - deg2 term - deg3 term
101 pub fn decompress(&self, hint: &Scalar) -> UniPoly {
102 let mut linear_term =
103 (*hint) - self.coeffs_except_linear_term[0] - self.coeffs_except_linear_term[0];
104 for i in 1..self.coeffs_except_linear_term.len() {
105 linear_term -= self.coeffs_except_linear_term[i];
106 }
107
108 let mut coeffs = vec![self.coeffs_except_linear_term[0], linear_term];
109 coeffs.extend(&self.coeffs_except_linear_term[1..]);
110 assert_eq!(self.coeffs_except_linear_term.len() + 1, coeffs.len());
111 UniPoly { coeffs }
112 }
113}
114
115impl AppendToPoseidon for UniPoly {
116 fn append_to_poseidon(&self, transcript: &mut PoseidonTranscript) {
117 // transcript.append_message(label, b"UniPoly_begin");
118 for i in 0..self.coeffs.len() {
119 transcript.append_scalar(&self.coeffs[i]);
120 }
121 // transcript.append_message(label, b"UniPoly_end");
122 }
123}
124
125impl AppendToTranscript for UniPoly {
126 fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript) {
127 transcript.append_message(label, b"UniPoly_begin");
128 for i in 0..self.coeffs.len() {
129 transcript.append_scalar(b"coeff", &self.coeffs[i]);
130 }
131 transcript.append_message(label, b"UniPoly_end");
132 }
133}
134
135#[cfg(test)]
136mod tests {
137
138 use ark_ff::One;
139
140 use super::*;
141
142 #[test]
143 fn test_from_evals_quad() {
144 // polynomial is 2x^2 + 3x + 1
145 let e0 = Scalar::one();
146 let e1 = Scalar::from(6);
147 let e2 = Scalar::from(15);
148 let evals = vec![e0, e1, e2];
149 let poly = UniPoly::from_evals(&evals);
150
151 assert_eq!(poly.eval_at_zero(), e0);
152 assert_eq!(poly.eval_at_one(), e1);
153 assert_eq!(poly.coeffs.len(), 3);
154 assert_eq!(poly.coeffs[0], Scalar::one());
155 assert_eq!(poly.coeffs[1], Scalar::from(3));
156 assert_eq!(poly.coeffs[2], Scalar::from(2));
157
158 let hint = e0 + e1;
159 let compressed_poly = poly.compress();
160 let decompressed_poly = compressed_poly.decompress(&hint);
161 for i in 0..decompressed_poly.coeffs.len() {
162 assert_eq!(decompressed_poly.coeffs[i], poly.coeffs[i]);
163 }
164
165 let e3 = Scalar::from(28);
166 assert_eq!(poly.evaluate(&Scalar::from(3)), e3);
167 }
168
169 #[test]
170 fn test_from_evals_cubic() {
171 // polynomial is x^3 + 2x^2 + 3x + 1
172 let e0 = Scalar::one();
173 let e1 = Scalar::from(7);
174 let e2 = Scalar::from(23);
175 let e3 = Scalar::from(55);
176 let evals = vec![e0, e1, e2, e3];
177 let poly = UniPoly::from_evals(&evals);
178
179 assert_eq!(poly.eval_at_zero(), e0);
180 assert_eq!(poly.eval_at_one(), e1);
181 assert_eq!(poly.coeffs.len(), 4);
182 assert_eq!(poly.coeffs[0], Scalar::one());
183 assert_eq!(poly.coeffs[1], Scalar::from(3));
184 assert_eq!(poly.coeffs[2], Scalar::from(2));
185 assert_eq!(poly.coeffs[3], Scalar::from(1));
186
187 let hint = e0 + e1;
188 let compressed_poly = poly.compress();
189 let decompressed_poly = compressed_poly.decompress(&hint);
190 for i in 0..decompressed_poly.coeffs.len() {
191 assert_eq!(decompressed_poly.coeffs[i], poly.coeffs[i]);
192 }
193
194 let e4 = Scalar::from(109);
195 assert_eq!(poly.evaluate(&Scalar::from(4)), e4);
196 }
197}