Delegating a Product of Group Exponentiations with Application to Signature Schemes (Submission to Special NutMiC 2019 Issue of JMC)

Journal of mathematical cryptology

article

Giovanni Di Crescenzo¹  Matluba Khodjaeva²  Delaram Kahrobaei³  Vladimir Shpilrain⁴ 

[1] Perspecta Labs Inc. Basking Ridge, United States of America;CUNY John Jay College of Criminal Justice. New York, United States of America;University of York. Heslington, United Kingdom;City University of New York. New, United States of America

关键词: Secure Delegation;    Modular Exponentiations;    Discrete Logarithms;    Cryptography;    Group Theory;    Elliptic Curves;   

DOI  :  10.1515/jmc-2019-0036

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Many public-key cryptosystems and, more generally, cryptographic protocols, use group exponentiations as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client (i.e., capable of performing a relatively small number of modular multiplications) delegates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client’s input exponent and security of the client’s output, in the sense of detecting, except for very small probability, any malicious server’s attempt to convince the client of an incorrect exponentiation result. Only recently, efficient protocols for the delegation of a fixed-based exponentiation, over cyclic and RSA-type groups with certain properties, have been presented and proved to satisfy both requirements. In this paper we show that a product of many fixed-base exponentiations, over a cyclic groups with certain properties, can be privately and securely delegated by keeping the client’s online number of modular multiplications only slightly larger than in the delegation of a single exponentiation. We use this result to show the first delegations of entire cryptographic schemes: the well-known digital signature schemes by El-Gamal, Schnorr and Okamoto, over the q -order subgroup in ℤ p , for p , q primes, as well as their variants based on elliptic curves. Previous efficient delegation results were limited to the delegation of single algorithms within cryptographic schemes.

【 授权许可】

CC BY|CC BY-NC-ND