Speeding up Exponentiation using an Untrusted Computational Resource

Marten van Dijk, Dwaine E. Clarke, Blaise Gassend, G. Edward Suh, Srinivas Devadas

Abstract: We present protocols for speeding up fixed-base variable-exponent exponentiation and variable-base fixed-exponent exponentiation using an untrusted computational resource. In the fixed-base protocols, the exponent may be blinded. In the variable-base protocols, the base may be blinded. The protocols are described for exponentiation in a cyclic group. We describe how to extend them to exponentiation modulo an integer where the modulus is the product of primes with single multiplicity. The protocols provide a speedup of \(\frac{3}{2}((\log k)-1)\) over the square-and-multiply algorithm, where k is the bitlength of the exponent.