Visible to the public Practical and Secure Outsourcing of Discrete Log Group Exponentiation to a Single Malicious Server

TitlePractical and Secure Outsourcing of Discrete Log Group Exponentiation to a Single Malicious Server
Publication TypeConference Paper
Year of Publication2017
AuthorsDi Crescenzo, Giovanni, Khodjaeva, Matluba, Kahrobaei, Delaram, Shpilrain, Vladimir
Conference NameProceedings of the 2017 on Cloud Computing Security Workshop
Conference LocationNew York, NY, USA
ISBN Number978-1-4503-5204-8
Keywordscontrol theory, cryptography, discrete logarithms, exponentiation, group theory, Human Behavior, human factor, modular exponentiations, privacy, pubcrawl, resilience, Resiliency, Scalability, secure delegation, secure outsourcing

Group exponentiation is an important 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 outsourced from a computationally weaker client to a computationally stronger server, possibly implemented in a cloud-based architecture. While preliminary solutions to this problem considered mostly honest servers, or multiple separated servers, some of which honest, solving this problem in the case of a single (logical), possibly malicious, server, has remained open since a formal cryptographic model was introduced in [20]. Several later attempts either failed to achieve privacy or only bounded by a constant the (security) probability that a cheating server convinces a client of an incorrect result. In this paper we solve this problem for a large class of cyclic groups, thus making our solutions applicable to many cryptosystems in the literature that are based on the hardness of the discrete logarithm problem or on related assumptions. Our main protocol satisfies natural correctness, security, privacy and efficiency requirements, where the security probability is exponentially small. In our main protocol, with very limited offline computation and server computation, the client can delegate an exponentiation to an exponent of the same length as a group element by performing an exponentiation to an exponent of short length (i.e., the length of a statistical parameter). We also show an extension protocol that further reduces client computation by a constant factor, while increasing offline computation and server computation by about the same factor.

Citation Keydi_crescenzo_practical_2017