On Cryptographic Schemes Based on Discrete Logarithms and Factoring
نویسنده
چکیده
At CRYPTO 2003, Rubin and Silverberg introduced the concept of torus-based cryptography over a finite field. We extend their setting to the ring of integers modulo N . We so obtain compact representations for cryptographic systems that base their security on the discrete logarithm problem and the factoring problem. This results in smaller key sizes and substantial savings in memory and bandwidth. But unlike the case of finite fields, analogous trace-based compression methods cannot be adapted to accommodate our extended setting when the underlying systems require more than a mere exponentiation. As an application, we present an improved, torus-based implementation of the ACJT group signature scheme.
منابع مشابه
Public-key cryptosystem design based on factoring and discrete logarithms - Computers and Digital Techniques, IEE Proceedings-
Most existing cryptosystem designs incorporate just one cryptographic assumption, such as factoring or discrete logarithms. These assumptions appear secure today; but, it is possible that efficient algorithms will be developed in the future lo break one or more of these assumptions. It is very unlikely that multiple cryptographic assumptions would simultaneously become easy to solve. Enhancing ...
متن کاملNew ID-Based Digital Signature Scheme on Factoring and Discrete Logarithms
The past years have seen many attempts to construct identity based signature schemes on a single hard problem, like factoring or discrete logarithms. But in the near future, those systems will no longer be secure if the solution of factoring or discrete logarithms problems is discovered. In this paper, we propose a new identification based signature scheme on factoring (FAC) problem and discret...
متن کاملMeta-He digital signatures based on factoring and discrete logarithms
This study investigates all variations of the He’s digital signature scheme based on factoring and discrete logarithms. In contrast to three modular exponentiation computation, the optimal two schemes of generalized He’s signature verification reveals that only two modular exponentiation is needed for signature verification. Key-Words: Digital signature, Batch verify, Computation complexity.
متن کاملNovel Digital Signature Schemes based on Factoring and Discrete Logarithms
In the paper, we propose a new digital signature scheme based on factoring and discrete logarithms. Specially, we prove that the security of the proposed signature scheme is based on both the security of the ElGamal signature scheme and the security of the modified OSS signature scheme. This is the first scheme which can be proved that its security is based on two hard problems. Like Meta-ElGam...
متن کاملCryptographic Protocols Based on Discrete Logarithms in Real-quadratic Orders
We generalize and improve the schemes of 4]. We introduce analogues of exponentiation and discrete logarithms in the principle cycle of real quadratic orders. This enables us to implement many cryptographic protocols based on discrete logarithms, e.g. a variant of the signature scheme of ElGamal 8].
متن کامل