org.bouncycastle.crypto.bls

Class Fp2Element

java.lang.Object

org.bouncycastle.crypto.bls.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 and 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.

Method Summary

Modifier and Type	Method and Description
Fp2Element	add(Fp2Element other)
java.math.BigInteger	c0()
java.math.BigInteger	c1()
boolean	equals(java.lang.Object other)
Fp2Element	frobenius() Frobenius: (c0 + c1*I)^p = c0 - c1*I when p ≡ 3 (mod 4), which holds for the BLS12-381 base field.
static Fp2Element	fromFp(java.math.BigInteger c0)
int	hashCode()
Fp2Element	inverse() Modular inverse: (c0 + c1*I)^-1 = (c0 - c1*I) / (c0^2 + c1^2).
boolean	isSquare()
boolean	isZero()
Fp2Element	modPow(java.math.BigInteger exponent) Modular exponentiation in Fp^2 by a non-negative integer exponent.
Fp2Element	mul(Fp2Element other) (a + b*I)(c + d*I) = (ac - bd) + (ad + bc)*I.
Fp2Element	mulFp(java.math.BigInteger fp) Multiply by a Fp scalar.
Fp2Element	neg()
static Fp2Element	of(java.math.BigInteger c0, java.math.BigInteger c1)
static Fp2Element	of(long c0, long c1)
int	sgn0() RFC 9380 sec. 4.1 sgn0 for m = 2.
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).
Fp2Element	square() (a + b*I)^2 = (a-b)(a+b) + 2ab*I.
Fp2Element	sub(Fp2Element other)
java.lang.String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

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()

add

public Fp2Element add(Fp2Element other)

sub

public Fp2Element sub(Fp2Element other)

neg

public Fp2Element neg()

mul

public Fp2Element mul(Fp2Element other)

(a + b*I)(c + d*I) = (ac - bd) + (ad + bc)*I.

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