Binary arithmetic | Multiplication | Computer arithmetic

Carry-less product

The carry-less product of two binary numbersis the result of carry-less multiplication of these numbers.This operation conceptually works like long multiplicationexcept for the fact that the carryis discarded instead of applied to the more significant position.It can be used to model operations over finite fields,in particular multiplication of polynomials from GF(2)[X],the polynomial ring over GF(2). The operation is also known as an XOR multiplication, as carry-discarding addition is equivalent to an exclusive or. (Wikipedia).

Carry-less product
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Related pages

Binary number | Finite field arithmetic | Galois/Counter Mode | Radix | GF(2) | Carry (arithmetic) | Finite field | Power of two | Polynomial ring | Checksum | Cryptography | Exclusive or