Secure fully-verifiable outsourcing of modular exponentiation: two servers check each other

• Published in: The Journal of supercomputing 2025-01, Vol.81 (1), Article 296
• Main Authors: Torki, Omid, Mala, Hamid, Ashouri-Talouki, Maede
• Format: Article
• Language: English
• Subjects: Cloud computing; Outsourcing; Verification
• ISSN: 0920-8542; 1573-0484
• DOI: 10.1007/s11227-024-06745-y

With the fast development of cloud computing, clients without enough computational power can widely outsource their heavy computations to cloud service providers. One of the most widely used and costly operations in cryptographic protocols is modular exponentiation, which can be computed at a lower cost by enjoying advantages of cloud computing, however, at the same time we need to address new challenges such as data privacy and verification of results. In this paper, first, we propose a secure outsourcing of single modular exponentiation protocol with verifiability one. Although the proposed single exponentiation scheme has the same verifiability as Ren’2018, but our scheme requires one less modular multiplication. However, the main contribution of this paper is proposing a scheme for outsourcing of multiplications of several modular exponentiations, hereafter called as composite exponentiation, which to the best of our knowledge, and is the first outsourcing scheme with full verification for composite exponentiation. As the evaluation results show, the advantages of this scheme, in comparison with state of the art schemes, are evident in terms of performance and verifiability criteria.