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

• Main Authors: Crescenzo Giovanni Di, Khodjaeva Matluba, Kahrobaei Delaram, Shpilrain Vladimir
• Format: Article
• Language: English
• Published: De Gruyter 2020-10-01
• Series: Journal of Mathematical Cryptology
• Subjects: secure delegation; modular exponentiations; discrete logarithms; cryptography; group theory; elliptic curves; 11t71; 94a60
• Online Access: https://doi.org/10.1515/jmc-2019-0036

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.