Add Fiat-Shamir Transformation into IOP #132
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Aug 19, 2024
algebra/src/polynomial/multivariate/multilinear/unified_field.rs
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algebra/src/polynomial/multivariate/multilinear/unified_field.rs
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algebra/src/polynomial/multivariate/multilinear/unified_field.rs
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| @@ -65,15 +72,82 @@ pub struct DecomposedBits<F: Field> { | |||
| /// number of variables of every polynomial | |||
| pub num_vars: usize, | |||
| /// batched plain deomposed bits, each of which corresponds to one bit decomposisiton instance | |||
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| /// batched plain deomposed bits, each of which corresponds to one bit decomposisiton instance | |
| /// batched plain deomposed bits, each of which corresponds to one bit decomposition instance |
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| for instance in &self.instances { | ||
| // For every bit, the reduced sum is $\sum_{x \in \{0, 1\}^\log M} eq(u, x) \cdot [\prod_{k=0}^B (d_i(x) - k)] = 0$ | ||
| // and the added product is r_i \cdot eq(u, x) \cdot [\prod_{k=0}^B (d_i(x) - k)] with the corresponding randomness | ||
| for bit in instance { | ||
| let mut product: Vec<_> = Vec::with_capacity(base + 1); | ||
| let mut op_coefficient = Vec::with_capacity(base + 1); | ||
| product.push(Rc::clone(&identity_func_at_u)); | ||
| op_coefficient.push((UF::one(), UF::zero())); | ||
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| let mut minus_k = F::zero(); | ||
| for _ in 0..base { | ||
| product.push(Rc::clone(bit)); | ||
| op_coefficient.push((UF::one(), UF::BaseField(minus_k))); | ||
| minus_k -= F::one(); | ||
| } | ||
| poly.add_product_with_linear_op(product, &op_coefficient, *r_iter.next().unwrap()); | ||
| } | ||
| } |
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I think here you are considering multiple instance of bit decomposition. For one instance, you are using r to combine them together. However, between instances, you just add the polys without random linear combination?
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Oh, it is already a random linear combination.
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