Journal
JOURNAL OF COMPUTER AND SYSTEM SCIENCES
Volume 121, Issue -, Pages 18-33Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcss.2021.04.006
Keywords
Computation outsourcing; Modular exponentiations; Weak-key attack; Coppersmith's method; Privacy-preserving
Funding
- National Natural Science Foundation of China [61702294]
- National Development Foundation of Cryptography [MMJJ20170126]
- Applied Basic Research Project of Qingdao City [17-1-1-10-jch]
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This study investigates the secure outsourcing of modular exponentiations in cryptography, identifying privacy issues and proposing attacks and revisions for certain protocols. The research shows that multiple modular exponentiation protocols become more efficient as the number of exponentiations increases.
We investigate the problem of securely outsourcing the modular exponentiations in cryptography to an untrusted server, and analyze the security and the efficiency of three privacy-preserving outsourcing protocols for exponentiations proposed in Ding et al. (2017) [18]. Based on Coppersmith's lattice-based method, we present heuristic polynomial-time and ciphertext-only weak-key attacks on these protocols, which shows that the recommended size of the secret keys in their protocols can not assure the input privacy of the exponents. Correspondingly, we explicitly estimate the size of the secure secret keys to circumvent our attacks, and analyze the efficiency of the revised protocols with security settings. Our theoretical analysis and experimental results demonstrate that the protocol of single modular exponentiation is unavailable, the protocol of simultaneous modular exponentiations is not so efficient as claimed but still available, and the protocol of multiple modular exponentiations becomes more efficient as the number of exponentiations increases. (C) 2021 Elsevier Inc. All rights reserved.
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