Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in number theory and cryptography
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A new public key cryptosystem based on elliptic curves over the ring Zn is described. The scheme can be used for both digital signature and encryption applications, does not expand the amount of data that needs to be transmitted and appears to be immune from homomorphic attacks. The main advantage of this system over other similar elliptic curve based systems is that there is very little restriction on the types of elliptic curves and types of primes (comprising the arithmetic modulus, n) that can be used. In addition, the system works on fixed elliptic curves. Problems associated with imbedding plaintext onto a curve are avoided by working within a multiple group structure. This enables the encryption and decryption operations to be performed on only the first coordinate of points on the given curve. The security of the system relies on the difficulty of factorising large composite numbers.