Skip to main content

field_sqrt_p3mod4

arcana::ecc::field

Function field_sqrt_p3mod4 

Source 
pub fn field_sqrt_p3mod4<const LIMBS: usize>(
    a: &FieldElement<LIMBS>,
    p: &[u64; LIMBS],
) -> FieldElement<LIMBS>
Expand description

Compute a square root of a in the prime field Fp, assuming p ≡ 3 (mod 4). Uses the closed-form identity

    y = a^((p+1)/4) mod p

When a is a quadratic residue, y * y ≡ a (mod p) and p - y is the other square root. When a is a non-residue, the returned value is not a square root of anything useful – callers MUST verify y*y == a mod p before trusting it.

All six curves currently shipped by this crate (P-256, P-384, secp256k1, brainpoolP{256,384,512}r1) have p ≡ 3 (mod 4), so this is the only sqrt helper we need. P-521 also satisfies p ≡ 3 (mod 4) and will reuse this function.

Used by SEC1 compressed-point decompression (recovering y from x).