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<ol class="chapter"><li class="chapter-item expanded "><a href="0_0_zero_network.html"><strong aria-hidden="true">1.</strong> Zero Network</a></li><li class="chapter-item expanded "><a href="1_0_overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="1_1_what_is_privacy.html"><strong aria-hidden="true">2.1.</strong> What is Privacy</a></li><li class="chapter-item expanded "><a href="1_2_hide_transfer_amount.html"><strong aria-hidden="true">2.2.</strong> Hide Transfer Amount</a></li><li class="chapter-item expanded "><a href="1_3_gas_limit.html"><strong aria-hidden="true">2.3.</strong> Gas Limit</a></li><li class="chapter-item expanded "><a href="1_4_zero_knowledge_scheme.html"><strong aria-hidden="true">2.4.</strong> Zero Knowledge Scheme</a></li><li class="chapter-item expanded "><a href="1_5_transaction_constraints.html"><strong aria-hidden="true">2.5.</strong> Transaction Constraints</a></li></ol></li><li class="chapter-item expanded "><a href="2_0_transaction_constraints.html"><strong aria-hidden="true">3.</strong> Transaction Constraints</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="2_1_confidential_transfer.html"><strong aria-hidden="true">3.1.</strong> Confidential Transfer</a></li><li class="chapter-item expanded "><a href="2_2_confidential_smart_contract.html"><strong aria-hidden="true">3.2.</strong> Confidential Smart Contract</a></li></ol></li><li class="chapter-item expanded "><a href="3_0_primitive.html"><strong aria-hidden="true">4.</strong> Primitive</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="3_1_crypto.html" class="active"><strong aria-hidden="true">4.1.</strong> Crypto</a></li><li class="chapter-item expanded "><a href="3_2_jubjub.html"><strong aria-hidden="true">4.2.</strong> Jubjub</a></li><li class="chapter-item expanded "><a href="3_3_bls12_381.html"><strong aria-hidden="true">4.3.</strong> Bls12 381</a></li><li class="chapter-item expanded "><a href="3_4_elgamal.html"><strong aria-hidden="true">4.4.</strong> ElGamal</a></li><li class="chapter-item expanded "><a href="3_5_pairing.html"><strong aria-hidden="true">4.5.</strong> Pairing</a></li></ol></li><li class="chapter-item expanded "><a href="4_0_pallet.html"><strong aria-hidden="true">5.</strong> Pallet</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="4_1_plonk.html"><strong aria-hidden="true">5.1.</strong> Plonk</a></li><li class="chapter-item expanded "><a href="4_2_encrypted_balance.html"><strong aria-hidden="true">5.2.</strong> Encrypted Balance</a></li><li class="chapter-item expanded "><a href="4_3_confidential_transfer.html"><strong aria-hidden="true">5.3.</strong> Confidential Transfer</a></li></ol></li><li class="chapter-item expanded "><a href="5_0_related_tools.html"><strong aria-hidden="true">6.</strong> Related Tools</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="5_1_stealth_address.html"><strong aria-hidden="true">6.1.</strong> Stealth Address</a></li><li class="chapter-item expanded "><a href="5_2_pedersen_commitment.html"><strong aria-hidden="true">6.2.</strong> Pedersen Commitment</a></li><li class="chapter-item expanded "><a href="5_3_non_interactive_zero_knowlege_proof.html"><strong aria-hidden="true">6.3.</strong> Non Interactive Zero Knowledge Proof</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="5_3_1_qap.html"><strong aria-hidden="true">6.3.1.</strong> QAP</a></li><li class="chapter-item expanded "><a href="5_3_2_polynomial_commitment.html"><strong aria-hidden="true">6.3.2.</strong> Polynomial Commitment</a></li><li class="chapter-item expanded "><a href="5_3_3_homomorphic_encryption.html"><strong aria-hidden="true">6.3.3.</strong> Homomorphic Encryption</a></li></ol></li></ol></li><li class="chapter-item expanded "><a href="6_0_tutorial.html"><strong aria-hidden="true">7.</strong> Tutorial</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="6_1_plonk_pallet.html"><strong aria-hidden="true">7.1.</strong> pallet-plonk</a></li><li class="chapter-item expanded "><a href="6_2_confidential_transfer.html"><strong aria-hidden="true">7.2.</strong> confidential_transfer</a></li></ol></li><li class="chapter-item expanded "><a href="7_0_frequent_errors.html"><strong aria-hidden="true">8.</strong> Frequent Errors</a></li></ol>
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<h1 class="menu-title">Zero Network Documentation</h1>
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<h1 id="crypto"><a class="header" href="#crypto">Crypto <a href="https://crates.io/crates/zero-crypto"><img src="https://img.shields.io/crates/v/zero-crypto.svg" alt="crates.io badge" /></a></a></h1>
<p>This crate provides basic cryptographic implementation as in <code>Field</code>, <code>Curve</code> and <code>Pairing</code>, <code>Fft</code>, <code>Kzg</code>, and also supports fully <code>no_std</code> and <a href="https://github.com/paritytech/parity-scale-codec"><code>parity-scale-codec</code></a>.</p>
<h2 id="usage"><a class="header" href="#usage">Usage</a></h2>
<h3 id="field"><a class="header" href="#field">Field</a></h3>
<p>The following <code>Fr</code> support four basic operation.</p>
<pre><code class="language-ignore">use zero_crypto::common::*;
use zero_crypto::dress::field::*;
use zero_crypto::arithmetic::bits_256::*;
use serde::{Deserialize, Serialize};
#[derive(Clone, Copy, Decode, Encode, Serialize, Deserialize)]
pub struct Fr(pub [u64; 4]);
const MODULUS: [u64; 4] = [
0xffffffff00000001,
0x53bda402fffe5bfe,
0x3339d80809a1d805,
0x73eda753299d7d48,
];
const GENERATOR: [u64; 4] = [
0x0000000efffffff1,
0x17e363d300189c0f,
0xff9c57876f8457b0,
0x351332208fc5a8c4,
];
/// R = 2^256 mod r
const R: [u64; 4] = [
0x00000001fffffffe,
0x5884b7fa00034802,
0x998c4fefecbc4ff5,
0x1824b159acc5056f,
];
/// R^2 = 2^512 mod r
const R2: [u64; 4] = [
0xc999e990f3f29c6d,
0x2b6cedcb87925c23,
0x05d314967254398f,
0x0748d9d99f59ff11,
];
/// R^3 = 2^768 mod r
const R3: [u64; 4] = [
0xc62c1807439b73af,
0x1b3e0d188cf06990,
0x73d13c71c7b5f418,
0x6e2a5bb9c8db33e9,
];
pub const INV: u64 = 0xfffffffeffffffff;
const S: usize = 32;
pub const ROOT_OF_UNITY: Fr = Fr([
0xb9b58d8c5f0e466a,
0x5b1b4c801819d7ec,
0x0af53ae352a31e64,
0x5bf3adda19e9b27b,
]);
impl Fr {
pub const fn to_mont_form(val: [u64; 4]) -> Self {
Self(to_mont_form(val, R2, MODULUS, INV))
}
pub(crate) const fn montgomery_reduce(self) -> [u64; 4] {
mont(
[self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0],
MODULUS,
INV,
)
}
}
fft_field_operation!(Fr, MODULUS, GENERATOR, INV, ROOT_OF_UNITY, R, R2, R3, S);
#[cfg(test)]
mod tests {
use super::*;
use paste::paste;
use rand_core::OsRng;
field_test!(bls12_381_scalar, Fr, 1000);
}
</code></pre>
<h3 id="curve"><a class="header" href="#curve">Curve</a></h3>
<p>The following <code>G1Affine</code> and <code>G1Projective</code> supports point arithmetic.</p>
<pre><code class="language-ignore">use crate::fq::Fq;
use crate::fr::Fr;
use zero_crypto::arithmetic::bits_384::*;
use zero_crypto::common::*;
use zero_crypto::dress::curve::*;
/// The projective form of coordinate
#[derive(Debug, Clone, Copy, Decode, Encode)]
pub struct G1Projective {
pub(crate) x: Fq,
pub(crate) y: Fq,
pub(crate) z: Fq,
}
/// The projective form of coordinate
#[derive(Debug, Clone, Copy, Decode, Encode)]
pub struct G1Affine {
pub(crate) x: Fq,
pub(crate) y: Fq,
is_infinity: bool,
}
curve_operation!(
Fr,
Fq,
G1_PARAM_A,
G1_PARAM_B,
G1Affine,
G1Projective,
G1_GENERATOR_X,
G1_GENERATOR_Y
);
#[cfg(test)]
mod tests {
#[allow(unused_imports)]
use super::*;
curve_test!(bls12_381, Fr, G1Affine, G1Projective, 100);
}
</code></pre>
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