Mathematical Problems and Algorithms for Timed-release Encryption

There are nowdays various e-business applications, such as sealedbid auctions and electronic voting, that require time-delayed decryption of encrypted data. The literature offers at least three main categories of protocols that provide such timed-release encryption (TRE). They rely either on forcing the recipient of a message to solve some time-consuming, non-paralellizable problem before being able to decrypt, or on the use of a trusted entity responsible for providing a piece of information which is necessary for decryption. This article discusses the mathematical background required for implementing TRE methods including factorization, quadratic residues and the bilinear Diffie-Hellman problems, along with a sample protocol for each of the approaches studied here. 2000 Mathematics Subject Classification: 11Y16, 14G50, 11D09, 11A51, 11A07.