Paper 2007/177

Space-Efficient Identity Based Encryption Without Pairings

Dan Boneh, Craig Gentry, and Michael 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 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.

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Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
dabo @ cs stanford edu
2007-05-20: received
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      author = {Dan Boneh and Craig Gentry and Michael Hamburg},
      title = {Space-Efficient Identity Based Encryption Without Pairings},
      howpublished = {Cryptology ePrint Archive, Paper 2007/177},
      year = {2007},
      note = {\url{}},
      url = {}
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