Improvement of Inverse Algorithm of Modulus in Finite Field for Elliptic Curve Encryption System
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In this paper, we mainly study the improvement of the finite field inverse algorithm of elliptic curve encryption system. In this paper, by studying the arithmetic operation of elliptic curve finite field, the idea of parallel modular multiplication is put forward, and the traditional Euclidean inverse algorithm is improved, so that it can complete modular and inverse operation at the same time. Combining the inverse operation in the prime field and the binary field can greatly improve the operation efficiency of the algorithm, which is conducive to improving the decryption speed of ECC. In addition, NTL has obvious advantages in the selection of irreducible polynomials, which is more convenient than Crypto++, and the operation efficiency of modular multiplication, modular square and modular remainder is also very high. In this way, the fast operation on the base field accelerates the dot multiplication operation on the elliptic curve, so NTL algorithm library has great advantages when applied to elliptic cryptosystems on GF(2m) field.
Elliptic curve, Gf(2m), Finite field, Inversion operation