International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Space-Efficient Identity Based Encryption Without Pairings

Dan Boneh
Craig Gentry
Mike Hamburg
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Abstract: 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 Z_N 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.
  title={Space-Efficient Identity Based Encryption Without Pairings},
  booktitle={IACR Eprint archive},
  note={ 13643 received 10 May 2007},
  author={Dan Boneh and Craig Gentry and Mike Hamburg},