Provably Secure Public Key Cryptosystem Based on Chebyshev Polynomials

Abstract-Chebyshev polynomials based public key cryptosystem (CPPKC), proposed by L. Kocarev in 2003, has emerged as a new research field in cryptography and attracted a lot of attentions in recent years. Although provable security in traditional public key cryptosystem has already been developed about twenty years, no relevant security proof research has been found about CPPKC. Aiming at the disability of CPPKC to resist against the adaptive chosen ciphertext attack, we construct a provably secure CPPKC, namely PS-CPPKC, which is designed utilizing the benefits of hash function and its security proof is completed under the Cheybshev Diffie-Hellman problem (CDHP) assumption by probabilistic analyses and computation in random oracle model. This is our primary exploration and it shows that provable security theory can combine well with CPPKC. Index Terms-Chebyshev polynomials, public key cryptosystem, chosen ciphertext attack, provable securit

A new RSA public key encryption scheme with chaotic maps

Public key cryptography has received great attention in the field of information exchange through insecure channels. In this paper, we combine the Dependent-RSA (DRSA) and chaotic maps (CM) to get a new secure cryptosystem, which depends on both integer factorization and chaotic maps discrete logarithm (CMDL). Using this new system, the scammer has to go through two levels of reverse engineering, concurrently, so as to perform the recovery of original text from the cipher-text has been received. Thus, this new system is supposed to be more sophisticated and more secure than other systems. We prove that our new cryptosystem does not increase the overhead in performing the encryption process or the decryption process considering that it requires minimum operations in both. We show that this new cryptosystem is more efficient in terms of performance compared with other encryption systems, which makes it more suitable for nodes with limited computational ability

Design of identity-based digital signature schemes using extended chaotic maps

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

CGST: Provably Secure Lightweight Certificateless Group Signcryption Technique Based on Fractional Chaotic Maps

In recent years, there has been a lot of research interest in analyzing chaotic constructions and their associated cryptographic structures. Compared with the essential combination of encryption and signature, the signcryption scheme has a more realistic solution for achieving message confidentiality and authentication simultaneously. However, the security of a signcryption scheme is questionable when deployed in modern safety-critical systems, especially as billions of sensitive user information is transmitted over open communication channels. In order to address this problem, a lightweight, provably secure certificateless technique that uses Fractional Chaotic Maps (FCM) for group-oriented signcryption (CGST) is proposed. The main feature of the CGST-FCM technique is that any group signcrypter may encrypt data/information with the group manager (GM) and have it sent to the verifier seamlessly. This implies the legitimacy of the signcrypted information/data is verifiable using the public conditions of the group, but they cannot link it to the conforming signcrypter. In this scenario, valid signcrypted information/data cannot be produced by the GM or any signcrypter in that category alone. However, the GM is allowed to reveal the identity of the signcrypter when there is a legal conflict to restrict repudiation of the signature. Generally, the CGST-FCM technique is protected from the indistinguishably chosen ciphertext attack (IND-CCA). Additionally, the computationally difficult Diffie-Hellman (DH) problems have been used to build unlinkability, untraceability, unforgeability, and robustness of the projected CGST-FCM scheme. Finally, the security investigation of the presented CGST-FCM technique shows appreciable consistency and high efficiency when applied in real-time security applications