New Algorithms for Secure Outsourcing of Modular Exponentiations

Abstract

Abstract. Modular exponentiations have been considered the most expensive operation in discrete-logarithm based cryptographic protocols. In this paper, we propose a new secure outsourcing algorithm for exponentiation modular a prime in the one-malicious model. Compared with the state-of-the-art algorithm [33], the proposed algorithm is superior in both efficiency and checkability. We then utilize this algorithm as a subroutine to achieve outsource-secure Cramer-Shoup encryptions and Schnorr signatures. Besides, we propose the first outsource-secure and efficient algorithm for simultaneous modular exponentiations. Moreover, we prove that both the algorithms can achieve the desired security notions.

Efficient and verifiable algorithms for secure outsourcing of cryptographic computations

“…Many algorithms have been proposed for outsourcing computation [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. They aim either to have a better outsourcing security model or to have more efficient constructions.…”

“…At ESORICS 2012, Chen et al [2] propose a more efficient construction than Hohenberger-Lysyanskaya's algorithm, where the probability of detecting malicious behavior is improved to 2/3. However, modular exponentiations can be computed by the client with O(log 2 (l)) multiplications.…”

“…Instead of having an adversary model, where distrustful servers are assumed not to collude, our algorithms borrow computing power from only a single untrusted cloud server. This constitutes a more realistic scenario when compared to the state-of-the-art algorithms in [2][3][4]. 2.…”

“…4. We emphasize further that although the existing solutions use two noncolluding malicious servers, they propose only 1/2, 2/3 or 3/4 probabilities for the checkability [2][3][4], respectively. Unlike all existing schemes, our algorithms have not only the best but also more importantly adjustable checkability.…”

Enhanced Secure Cloud Data Protection Model by Integrating Dual System Encryption Technology With Selective Proof Technique.

“…It answered the question: Can message-locked encryption be secure for lock dependent message [19]. The tag randomization design makes the fully random scheme, R-MLE2 for short, satisfy the standard secure notion of data confidentiality.…”