Adriana Lopez

Space-Efficient Identity Based Encryption Without Pairings

D. Boneh, C. Gentry, and M. Hamburg

Identity Based Encryption (IBE) systems are often constructed using
bilinear maps (a.k.a. pairings) on elliptic curves. One exception is
an elegant system due to Cocks which builds an IBE based on the
quadratic residuosity problem modulo an RSA composite N. The Cocks
system, however, produces long ciphertexts. Since the introduction of
the Cocks system in 2001 it has been an open problem to construct a
space efficient IBE system without pairings. In this paper we present
an IBE system in which ciphertext size is short: an encryption of an
l-bit message consists of a single element in ZN plus l+1 additional
bits. Security, as in the Cocks system, relies on the quadratic
residuosity problem. The system is based on the theory of ternary
quadratic forms and as a result, encryption and decryption are slower
than in the Cocks system.