Efficient and verifiable algorithms for secure outsourcing of cryptographic computations

Reducing computational cost of cryptographic computations for resource-constrained devices is an active research area. One of the practical solutions is to securely outsource the computations to an external and more powerful cloud server. Modular exponentiations are the most expensive computation from the cryptographic point of view. Therefore, outsourcing modular exponentiations to a single, external and potentially untrusted cloud server while ensuring the security and privacy provides an efficient solution. In this paper, we propose new efficient outsourcing algorithms for modular exponentiations using only one untrusted cloud server. These algorithms cover public-base and private-exponent, private-base and public-exponent, private-base and private-exponent, more generally private-base and private-exponents simultaneous modular exponentiations. Our algorithms are the most efficient solutions utilizing only one single untrusted server with the best checkability probabilities. Furthermore, unlike existing schemes, which have fixed checkability probability, our algorithms provide adjustable predetermined checkability parameters. Finally, we apply our algorithms to outsource oblivious transfer protocols and blind signatures which are expensive primitives in modern cryptography.