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 represents the polynomial . The CLMUL instruction also allows a more efficient implementation of the closely related multiplication of larger finite fields GF(2k) 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(2k) 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".
^"Intel Software Network". Intel. Archived from the original on 2008-04-07. Retrieved 2008-04-05.
^Shay Gueron; Michael E. Kounavis (2014-04-20). "Intel Carry-Less Multiplication Instruction and its Usage for Computing the GCM Mode – Rev 2.02" (PDF). Intel. Archived from the original on 2019-08-06.
^"Fast CRC Computation for Generic Polynomials Using PCLMULQDQ" (PDF).
^Vlad Krasnov (2015-07-08). "Fighting Cancer: The Unexpected Benefit Of Open Sourcing Our Code". CloudFlare. Retrieved 2016-09-04.
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