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^[1] 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.^[2]

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,^[3] including those used to implement the LZ77 sliding window DEFLATE algorithm in zlib and pngcrush.^[4]

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