Package org.bouncycastle.crypto.bls

Class Fp2Element

  • public final class Fp2Element
extends java.lang.Object
    Immutable element of Fp^2 = Fp[I] / (I^2 + 1), used as the base field of BLS12-381 G2.

    All operations reduce modulo p eagerly. Internally the two Fp components are stored as plain BigInteger values.

    • Field Summary

      Fields 
      Modifier and Type Field Description
      static Fp2Element ONE
      The Fp^2 one element (1 + 0*I).
      static java.math.BigInteger P
      Field characteristic, identical to the BLS12-381 base field p.
      static Fp2Element ZERO
      The Fp^2 zero element.

    • Field Detail

      • P

        public static final java.math.BigInteger P
        Field characteristic, identical to the BLS12-381 base field p.

      • ZERO

        public static final Fp2Element ZERO
        The Fp^2 zero element.

      • ONE

        public static final Fp2Element ONE
        The Fp^2 one element (1 + 0*I).

    • Method Detail

      • of

        public static Fp2Element of​(java.math.BigInteger c0,
                            java.math.BigInteger c1)

      • of

        public static Fp2Element of​(long c0,
                            long c1)

      • fromFp

        public static Fp2Element fromFp​(java.math.BigInteger c0)

      • c0

        public java.math.BigInteger c0()
        Returns:
        real component (the c0 in c0 + c1*I).

      • c1

        public java.math.BigInteger c1()
        Returns:
        imaginary component (the c1 in c0 + c1*I).

      • isZero

        public boolean isZero()

      • mulFp

        public Fp2Element mulFp​(java.math.BigInteger fp)
        Multiply by a Fp scalar.

      • square

        public Fp2Element square()
        (a + b*I)^2 = (a-b)(a+b) + 2ab*I.

      • frobenius

        public Fp2Element frobenius()
        Frobenius: (c0 + c1*I)^p = c0 - c1*I when p ≡ 3 (mod 4), which holds for the BLS12-381 base field.

      • inverse

        public Fp2Element inverse()
        Modular inverse: (c0 + c1*I)^-1 = (c0 - c1*I) / (c0^2 + c1^2).

      • modPow

        public Fp2Element modPow​(java.math.BigInteger exponent)
        Modular exponentiation in Fp^2 by a non-negative integer exponent.

      • sgn0

        public int sgn0()
        RFC 9380 sec. 4.1 sgn0 for m = 2. 
           sign_0 = c0 mod 2
   zero_0 = (c0 == 0)
   sign_1 = c1 mod 2
   return sign_0 OR (zero_0 AND sign_1)

      • sqrtOrNull

        public Fp2Element sqrtOrNull()
        Tries to compute a square root of this in Fp^2, using the Wahby-Boneh algorithm specialised to p ≡ 3 (mod 4) ("Fast and simple constant-time hashing to the BLS12-381 elliptic curve", Algorithm 1).
        Returns:
        a square root, or null if this is not a square.

      • isSquare

        public boolean isSquare()

      • equals

        public boolean equals​(java.lang.Object other)
        Overrides:
        equals in class java.lang.Object

      • hashCode

        public int hashCode()
        Overrides:
        hashCode in class java.lang.Object

      • toString

        public java.lang.String toString()
        Overrides:
        toString in class java.lang.Object