An Identity Based Encryption Scheme based on Jacobi Symbols

Vishal Saraswat

In an offline public key system, in order to send encrypted data it is necessary to know the public key of the recipient. This usually necessitates the holding of directories of public keys and their cetificates. To simplify certificate management, in 1984 Adi Shamir [2] asked for a public key encryption scheme in which the public key can be any arbitrary string.

In this talk we present Clifford Cocks' identity-based encryption (CC-IBE) scheme [1] based on Jacobi symbols which is related to the difficulty of solving the quadratic residuosity problem. In an identity-based encryption (IBE) scheme, the sender Alice can use the receiver Bob's identifier information such as email or IP address, or any arbitrary string, to encrypt a message. The receiver Bob, having obtained a private key associated with his identifier information from a trusted third party called the Private Key Generator (PKG), can decrypt the ciphertext.

[1] C. Cocks, An Identity Based Encryption Echeme based on Quadratic Residues, Eighth IMA International Conference on Cryptography and Coding, Dec. 2001, Royal Agricultural College, Cirencester, UK.

[2] A. Shamir, Identity-based Cryptosystems and Signature Schemes, Advances in Cryptology - Proc. of CRYPTO 84, LNCS 196, Springer-Verlag.

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