All-in-one irreducible polynomial based finite field multiplier

Abstract

The invention relates to an all-in-one irreducible polynomial based finite field multiplier which comprises a controller, an input control module, an output control module, a finite field multiplier and an operation module, wherein the controller is used for controlling and scheduling data transmission among the input control module, the output control module and the finite field multiplier; the input control module is used for inputting a multiplication operation number a(x) and a multiplication operation number b(x) when detecting that a finite field GF(2n) has an all-in-one irreducible polynomial; the finite field multiplier is used for calling the operation module to carry out finite field multiplication operation on the multiplication operation number a(x) and the multiplication operation number b(x) to obtain a multiplication operation result c(x); the operation module is used for implementing and logical operation, exclusive or logic operation and modular operation; the output control module is used for outing the multiplication operation result c(x). By adopting the multiplier, the operation efficiency of finite field multiplication is improved.

Description

technical field

[0001] The invention relates to the field of computer technology, in particular to a finite-field multiplier based on all-one irreducible polynomials. Background technique

[0002] A finite field is a field containing only a finite number of elements, first discovered by Galois, so a finite field is also called a Galois field. Its characteristic is that the results of operations such as addition, multiplication, inversion, and division of finite fields are elements of finite fields. Therefore, finite field operations generally require irreducible polynomials to participate in the operation to ensure that the result of the operation is still on the field. Irreducible polynomials, also known as reduced polynomials, are polynomials with rational coefficients whose degree is greater than zero. Its characteristic is that it cannot be decomposed into two polynomials with rational coefficients of lower degree but both are greater than zero. In a finite field, an i...

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