CLMUL instruction set

Carry-less Multiplication (CLMUL) is an extension to the x86 instruction set used by microprocessors from Intel and AMD which was proposed by Intel in March 2008 and made available in the Intel Westmere processors announced in early 2010. Mathematically, the instruction implements multiplication of polynomials over the finite field GF(2) where the bitstring ${\displaystyle a_{0}a_{1}\ldots a_{63}}$ represents the polynomial ${\displaystyle a_{0}+a_{1}X+a_{2}X^{2}+\cdots +a_{63}X^{63}}$. The CLMUL instruction also allows a more efficient implementation of the closely related multiplication of larger finite fields GF(2^k) than the traditional instruction set.

One use of these instructions is to improve the speed of applications doing block cipher encryption in Galois/Counter Mode, which depends on finite field GF(2^k) multiplication. Another application is the fast calculation of CRC values, including those used to implement the LZ77 sliding window DEFLATE algorithm in zlib and pngcrush.

ARMv8 also has a version of CLMUL. SPARC calls their version XMULX, for "XOR multiplication".