Elliptic Curve Cryptosystems
Copyright policy )Elliptic Curve Cryptosystems
We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially over GF ( 2 n ) {\text {GF}}({2^n}) . We discuss the question of primitive points on an elliptic curve modulo p, and give a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point.
Cryptography, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Public key cryptosystems, group of points of an elliptic curve over a large finite field
Cryptography, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Public key cryptosystems, group of points of an elliptic curve over a large finite field
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