GFNI instruction set

Galois Field New Instructions is a subset extension from Intel to accelerate cryptographic applications. However its instructions have additional unexpected beneficial purposes in bit manipulation, and the instructions can be present in other ISAs

Description

The GFNI extension comprises three instructions, VGF2P8AFFINEINVQB,^[1] VGF2P8AFFINEQB^[2] and VGF2P8MULB.^[3] They are useful for cryptography,^[4] as they can be used to implement Rijndael-style S-boxes such as those used in AES, Camellia, and SM4.^[5] These instructions are also used for bit manipulation in networking and signal processing: bits can be arbitrarily reordered, copied, inverted, cleared, or set with them.^[4]

GFNI is a standalone instruction set extension and can be enabled separately from AVX or AVX-512. Depending on whether AVX and AVX-512F support is indicated by the CPU, GFNI support enables legacy (SSE), VEX or EVEX-coded instructions operating on 128, 256 or 512-bit vectors.

Instruction	Description
VGF2P8AFFINEINVQB	Galois field affine transformation inverse[1]
VGF2P8AFFINEQB	Galois field affine transformation[2]
VGF2P8MULB	Galois field multiply bytes[3]

Additional uses

GNFI was originally intended to help accelerate for example Rijndael (AES) GF(2^8) arithmetic: Rijndael has an explicit GF(2^8) reducing polynomial of 0x11B. However surprising number of additional uses have emerged:

• An Intel guide^[6] lists parallel 5-bit byte-wise sign-extension, general bit-clear insert set and invert,
• Parallel Count Leading/Trailing Zero Bits (Byte-wise), Arbitrary GF(2^N) multiplication, Fixed 2-bit Packed Arithmetic, Byte-wise variable shift, which relies on pre-truncating the inputs to ensure the polynomial reduction is not triggered.^[7]
• Bit-reversal^[8]
• SM4, Reed Solomon, RAID6 ^[9]
• Vector bit-reverse https://reviews.llvm.org/D91515?id=305411
• bmatflip and bmatxor is found in the Cray XMT
• Power ISA vgbbd Chapter 6. Vector Facility, Book 1 p. 445

See also

• bit manipulation – Algorithmically modifying data below the word level
• AVX512 – Instruction set extension by IntelPages displaying short descriptions of redirect targets
• AVX2 – Instructions for the x86 microprocessorsPages displaying short descriptions of redirect targets
• Finite_field_arithmetic – Arithmetic in a field with a finite number of elements
• GF(2) – Finite field of two elements