# Information Security and Cryptography Research Group

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

### Kenji Koyama, Ueli Maurer, Tatsuaki Okamoto, and Scott Vanstone

Advances in Cryptology — CRYPTO '91, Lecture Notes in Computer Science, Springer-Verlag, vol. 576, pp. 252–266, Aug 1991.

Three new trapdoor one-way functions are proposed that are based on elliptic curves over the ring $\Z_n$. 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.

## BibTeX Citation

@inproceedings{KMOV91,
author       = {Kenji Koyama and Ueli Maurer and Tatsuaki Okamoto and Scott Vanstone},
title        = {New Public-Key Schemes Based on Elliptic Curves over the Ring ${Z}_n$},
editor       = {J. Feigenbaum},
booktitle    = {Advances in Cryptology --- CRYPTO~'91},
pages        = {252--266},
series       = {Lecture Notes in Computer Science},
volume       = {576},
year         = {1991},
month        = {8},
publisher    = {Springer-Verlag},
}