Efficient and Secure Delegation to a Single Malicious Server: Exponentiation over Non-abelian Groups
Group exponentiation is an important and expensive operation used in many public-key cryptosystems and, more generally, cryptographic protocols. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that this operation is delegated from a computationally weaker client to a computationally stronger server. Solving this problem in the case of a single, possibly malicious, server, has remained open since a formal model was introduced in . Recently, in  we proposed practical and secure solutions applicable to a class of cyclic groups. In this paper, we propose efficient and secure solutions applicable to a large class of multiplicative groups, possibly beyond groups currently subject to quantum cryptanalysis attacks.
- 1.Anshel, I., Atkins, D., Goldfeld, D., Gunnels, P.E.: Post Quantum Group Theoretic Cryptography, November 2016. https://bit.ly/2svnv8z
- 3.Cavallo, B., Di Crescenzo, G., Kahrobaei, D., Shpilrain, V.: Efficient and secure delegation of group exponentiation to a single server. In: Mangard, S., Schaumont, P. (eds.) RFIDSec 2015. LNCS, vol. 9440, pp. 156–173. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24837-0_10CrossRefGoogle Scholar
- 9.Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of 35th IEEE Symposium on Foundations of Computer Science (FOCS 1994), pp. 124–134 (1994)Google Scholar
- 10.Di Crescenzo, G., Khodjaeva, M., Kahrobaei, D., Shpilrain, V.: Practical and secure outsourcing of discrete log group exponentiation to a single malicious server. In: Proceedings of 9th ACM Cloud Computing Security Workshop (CCSW), pp. 17–28 (2017)Google Scholar