Design of identity-based digital signature schemes using extended chaotic maps.
SK Hafizul Islam · IACR Cryptology ePrint Archive · 2014
Inspired from the Identity-based cryptosystem proposed by Adi Shamir, and Boneh and Franklin, this paper designed a new Identity-based digital signature (ECM-IDS) scheme using extended chaotic maps. The ECM-IDS scheme is secure based on the difficulties of integer factorization problem. In the public key infrastructure-based cryptosystems, the public key certificate that is generated and signed by a certificate authority (CA) is required for authentication of the public keys of the entities, and, as a result, it creates a heavy management burden for maintaining and using the public key certificate by developing a global infrastructure. As a remedy, Shamir (1) proposed the concept of an identity-based cryptosystem (IBC) that supports the users' authentication through the use of a public identity. In other words, a user's public key in IBC is computed from an email identity, a social security number, a passport number or other identifiers and a private key generator (PKG); a trusted third party generates the user's private key by using the user's identity and his/her master private key. The private key generated by PKG is communicated to the user through a secure channel, for which its legitimacy can be verified by the user publicly. However, as such, no practical implementation for IBC was proposed by Shamir, and in 2001, Boneh and Franklin (2) first proposed a practical identity-based encryption (IBE) using elliptic curve bilinear pairing. The IBE scheme is secure based on the Bilinear Diffie Hellman (BDH) assumption. Recently, the extended chaotic maps are extensively studied in cryptography, many schemes (3, 4, 5, 6, 7, 8, 9, 10, 11, 12) have been proposed in cryptography based on extended chaotic maps. In 2004, Fee and Monagan (17) extended the RSA cryptosystem using extended chaotic maps and its security is based on the integer factorization problem (IFP) as in original RSA system. Based on the works (1, 2, 17), this paper designed a new ECM-IDS scheme. The security of the ECM-IDS scheme is based on the hardness assumption of IFP problem. The paper is organized in the following ways. The Section 2, described the theory and properties of the extended chaotic maps and two computational problems. The Section 3 described the proposed ECM-IDS scheme and its security analysis. Finally, the Section 4 concludes the paper.