Identity-Based Identification and Signature Schemes using Error Correcting Codes

Abstract

Abstract. In this paper, we propose a new identity-based authentica-tion (and signature) scheme based on error-correcting codes. This schemeis up to date the first identity-based scheme not based on number theory.The scheme combines two well known code-based schemes: the signaturescheme of Courtois, Finiasz and Sendrier and the zero-knowledge au-thentication scheme of Stern (which may also be used for signature).The scheme inherits from the characteristics of the previous schemes: ithas a large public key of order 1Mo and necessitates a certain number ofexchange rounds. The scheme can also work in signature but leads to avery large signature of size 1Mo.Keywords : Signature, Authentication, Identity based scheme, Correct-ing codes, Stern, Niederreiter. 1 Introduction Themostcriticalpointofclassicalpublickeycryptography(RSA,ElGamal...)is in the management of the authenticity of the public key. In fact, if Alice man-ages to take Bob’s identity by cheating her own public key as Bob’s one, shewould be able to decipher all messages sent to Bob and to sign any messageusing the stolen identity.In 1984, Shamir introduced the concept of IDentity-based Public Key Cryp-tography ID-PKC [15] in order to simplify the management and the authenti-cation of the public key, which time passing by, had become more and morecomplex.In the ID-PKC scheme of Shamir, the public key of an user is undeniablylinked to his identity on the network (user-id): it can be a concatenation ofany publicly known information: his name, his e-mail, his phone number, etc ...