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Publications: Abstract

New Public-Key Schemes Based on Elliptic Curves over the Ring ${Z}_n$

Kenji Koyama and Ueli Maurer and Tatsuaki Okamoto and Scott Vanstone

Three new trapdoor one-way functions are proposed that are based on elliptic curves over the ring $\zn$. The first class of functions is a naive construction, which can be used only in a digital signature scheme, and not in a public-key cryptosystem. The second, preferred class of function, does not suffer from this problem and can be used for the same applications as the RSA trapdoor one-way function, including zero-knowledge identification protocols. The third class of functions has similar properties to the Rabin trapdoor one-way functions. Although the security of these proposed schemes is based on the difficulty of factoring $n$, like the RSA and Rabin schemes, these schemes seem to be more secure than those schemes from the viewpoint of attacks without factoring such as low multiplier attacks.