Recently, Ranjan proposed a novel public key encryption technique based on multiple chaotic systems [Phys Lett 2005;95]. Unfortunately, Wang soon gave a successful attack on its special case based on Parseval’s theorem [Wang K, Pei W, Zhou L, et al. Security of public key encryption technique based on multiple chaotic system. Phys Lett A, in press]. In this letter, we give an improved example which can avoid the attack and point out that Wang cannot find the essential drawback of the technique. However, further experimental result shows Ruanjan’s encryption technique is inefficient, and detailed theoretic analysis shows that the complexity to break the cryptosystem is overestimated.

Cryptanalysis of the public key encryption based on multiple chaotic systems

A novel key agreement protocol based on chaotic maps

The recent proliferation of mobile devices, such as smartphones and wearable devices has given rise to crowdsourcing Internet of Things (IoT) applications. E-healthcare service is one of the important services for the crowdsourcing IoT applications that facilitates remote access or storage of medical server data to the authorized users (for example, doctors, patients, and nurses) via wireless communication. As wireless communication is susceptible to various kinds of threats and attacks, remote user authentication is highly essential for a hazard-free use of these services. In this paper, we aim to propose a new secure three-factor user remote user authentication protocol based on the extended chaotic maps. The three factors involved in the proposed scheme are: 1) smart card; 2) password; and 3) personal biometrics. As the proposed scheme avoids computationally expensive elliptic curve point multiplication or modular exponentiation operation, it is lightweight and efficient. The formal security verification using the widely-accepted verification tool, called the ProVerif 1.93, shows that the presented scheme is secure. In addition, we present the formal security analysis using the both widely accepted real-or-random model and Burrows–Abadi–Needham logic. With the combination of high security and appreciably low communication and computational overheads, our scheme is very much practical for battery limited devices for the healthcare applications as compared to other existing related schemes.

Chaotic Map-Based Anonymous User Authentication Scheme With User Biometrics and Fuzzy Extractor for Crowdsourcing Internet of Things

A user friendly mutual authentication and key agreement scheme for wireless sensor networks using chaotic maps

An improved key agreement protocol based on chaos

Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which makes possible implementing a trapdoor mechanism. In this paper, we study a public-key cryptosystem based on such polynomials, which provides both encryption and digital signature. The cryptosystem works on real numbers and is quite efficient. Unfortunately, from our analysis, it comes up that it is not secure. We describe an attack which permits to recover the corresponding plaintext from a given ciphertext. The same attack can be applied to produce forgeries if the cryptosystem is used for signing messages. Then, we point out that also other primitives, a Diffie-Hellman like key agreement scheme and an authentication scheme, designed along the same lines of the cryptosystem, are not secure due to the aforementioned attack. We close the paper by discussing the issues and the possibilities of constructing public-key cryptosystems on real numbers.

P. Bergamo

Papers

Security of public-key cryptosystems based on Chebyshev polynomials