Boneh-Gentry-Hamburg\u27s Identity-based Encryption Schemes Revisited

Abstract

BasicIBE and AnonIBE are two space-efficient identity-based encryption (IBE) schemes based on quadratic residues, proposed by Boneh, Gentry, and Hamburg, and closely related to Cocks\u27 IBE scheme. BasicIBE is secure in the random oracle model under the quadratic residuosity assumption, while AnonIBE is secure in the standard model under the interactive quadratic residuosity assumption. In this paper we revise the BasicIBE scheme and we show that if the requirements for the deterministic algorithms used to output encryption and decryption polynomials are slightly changed, then the scheme\u27s security margin can be slightly improved