New Results on Identity-based Encryption from Quadratic Residuosity

This paper surveys the results obtained so far in designing identity-based encryption (IBE) schemes based on the quadratic residuosity assumption (QRA). We begin by describing the first such scheme due to Cocks, and then we advance to the novel idea of Boneh, Gentry and Hamburg. Major improvements of the Boneh-Gentry-Hamburg scheme are then recalled. The recently revealed algebraic torus structures of the Cocks scheme allows for a better understanding of this scheme, as well as for new applications of it such as homomorphic and anonymous variants of it