MapReduce for Elliptic Curve Discrete Logarithm Problem

Elliptic curve based cryptography has attracted a lot of attention because these schemes usually require less storage than those based on finite field. It is also used to construct bilinear pairing, which is an essential tool to construct various cryptography schemes. The security of a large portion of these schemes depends on the hardness of ECDLP. Unlike discrete logarithm problem on finite field and integer factorization problem, currently there is no sub-exponential algorithm for general ECDLP, and parallel collision search is the most effective approach. Using parallel collision search for ECDLP is not only computation intensive but also storage intensive. Therefore, it requires a large number of machines to collaborate to finish the job. Considering all these requirements, we propose a solution for ECDLP using MapReduce and parallel collision search in the cloud environment, which can be scaled to involve a huge number of computation nodes. We implement the solution using Amazon EC2, and the experiment results show its scalability and effectiveness.