Mathematical problems and algorithms for timed − release encryption

Abstract

There are nowadays various e-business applications, such as sealed-bid 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-parallelizable problem before being able to decrypt or on the use of a trusted entity responsible for providing a piece of information that 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.