Space-Efficient Identity Based Encryption Without Pairings

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 f. -bit message consists of a single element in Z/NZ plus lscr + 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.

Authors

• Dan Boneh
• Craig Gentry
• Michael Hamburg

Keywords

• Identity-based encryption
• Computer science
• Public key
• Elliptic curves
• Application software
• Public key cryptography
• Elliptic curve cryptography
• Computer security
• Pairing
• Elliptic Curve
• Bilinear Map
• Encryption And Decryption
• Additional Bits
• Square Root
• Random Model
• Standard Model
• Plaintext
• Hash Function
• Secret Key
• Usual Way
• Global Field
• Definition Of Conditions
• Security Parameter
• Random Bits
• Random Oracle
• Signature Scheme
• Random Oracle Model
• Encryption Time