Polynomial-based GF(2^n) multiplier

Abstract

The invention discloses a polynomial-based GF(2^n) multiplier. The multiplier is used for calculating a product of an element A and an element B (shown in the description) in a polynomial ring R[x]. The multiplier comprises a quotient solving module, an intermediate modular multiplication calculation module and a summation module, wherein the quotient solving module is used for calculating a quotient q obtained after the product AB of the polynomial A and the polynomial B (shown in the description) for modular multiplication is divided by an n-degree polynomial (f(x)-1); the intermediate modular multiplication calculation module is used for calculating modular multiplication between the product AB of the polynomial A and the polynomial B and the polynomial (f(x)-1) to obtain an intermediate modular value (c+q); and the input end of the summation module is connected with the output end of the intermediate modular multiplication calculation module and the output end of the quotient solving module, and the summation module is used for subtracting the quotient q from the intermediate modular value (c+q) to obtain a modular multiplication value c of the product AB of the polynomial A and the polynomial B relative to a polynomial f(x). Through the multiplier, a direct module solving step relative to the polynomial f(x) is unavailable, less XOR gates and AND gates are available on average, and therefore the space complexity of the multiplier is lowered under the condition that time complexity is not improved. The complexity of a multiplier integrated circuit is lowered, and the overall volume of the multiplier is shrunk beneficially.

Description

technical field [0001] The invention relates to the technical field of digital signal processing, in particular to a polynomial base GF(2^n) multiplier. Background technique [0002] f(x)=x n +x k +1(n>2) is an irreducible polynomial of degree n on GF(2), then the finite field GF(2 n ) := GF(2)[x] / (f(u)) All elements under the polynomial basis {x i |0≤i≤n-1} to represent. For two elements in a given domain and Then calculate the product of A and B The conventional method is accomplished in the following two steps. [0003] (1) Traditional polynomial multiplication: Each item is specifically: [0004] [0005] (2) Modulo operation [0006] [0007] However, to perform the above-mentioned modular operation, more XOR gates and AND gates need to be arranged in the calculation circuit of the multiplier, which takes up a lot of space and is not conducive to the reduction of the size of the multiplier. Contents of the invention [0008] Based on this, it i...

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Problems solved by technology

[0007] However, to perform the above-mentioned modulo calculation, more XOR gates and AND gates need to be installed in the calculation circuit of the multiplier, which takes up more space and is not conducive to the reduction of the size of the multiplier.

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