Fp12 (Bouncy Castle Library 1.86 API Specification)

java.lang.Object
- org.bouncycastle.math.ec.sm9.Fp12

```
public class Fp12
extends java.lang.Object
```
Element of F_p12 = F_p4[w]/(w^3 - v), i.e. w^3 = v, for SM9 (GM/T 0044.5-2016, 1-2-4-12 tower). This is the pairing target group G_T. Written a + b*w + c*w^2 with a the low and c the high (w^2-coefficient) dimension, a, b, c in Fp4. Immutable.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`boolean`	`equals(java.lang.Object other)`
`int`	`hashCode()`
`Fp12`	`multiply(Fp12 o)`
`Fp12`	`pow(java.math.BigInteger e)`	Variable-time exponentiation, for PUBLIC exponents only (the pairing's Frobenius and final exponentiation, and g^h' in signature verification).
`Fp12`	`powSecure(java.math.BigInteger e)`	Constant-pattern exponentiation for SECRET exponents (a Montgomery ladder running a fixed number of iterations - the SM9 group order bit length - with exactly one multiply and one square per bit regardless of the exponent bits), used for w = g^r where r is a signing nonce or ephemeral secret.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - multiply
```
public Fp12 multiply(Fp12 o)
```
  - pow
```
public Fp12 pow(java.math.BigInteger e)
```
    Variable-time exponentiation, for PUBLIC exponents only (the pairing's Frobenius and final exponentiation, and g^h' in signature verification). For secret exponents use powSecure(java.math.BigInteger).
  - powSecure
```
public Fp12 powSecure(java.math.BigInteger e)
```
    Constant-pattern exponentiation for SECRET exponents (a Montgomery ladder running a fixed number of iterations - the SM9 group order bit length - with exactly one multiply and one square per bit regardless of the exponent bits), used for w = g^r where r is a signing nonce or ephemeral secret. Unlike pow(java.math.BigInteger), the operation pattern does not leak the exponent's Hamming weight or individual bits. The exponent must satisfy 0 <= e < N (every SM9 secret exponent is reduced mod the group order N).
    NOTE: the underlying F_p arithmetic is BigInteger-based and is not itself constant time, so this removes the exponent-structure leak but not every timing side channel.
  - 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