Chaotic map based key agreement with/out clock synchronization

In order to address Bergamo et al.’s attack, Xiao et al. proposed a key agreement protocol using chaotic maps. Han then presented three attacks on Xiao et al.’s protocol. To enhance the security of key agreement based on chaotic maps, Chang et al. proposed a new key agreement using passphrase, which works in clock synchronization environment. However, their protocol still has some issues: one is its passphrase is not easy to remember and much longer than password; the second one is it cannot resist guessing attack if the constructed passphrase is easy to remember and also has already existed in some rational dictionaries; the third one is it cannot work without clock synchronization. In this paper, we will present two different key agreement protocols, which can resist guessing attack. The first one works in clock synchronization environment. The second one can work without clock synchronization. They both use authenticated password for secure communications. The protocols are secure against replaying attacks and a shared session key can be established.     

An Efficient Protocol for Authenticated Key Agreement

This paper proposes an efficient two-pass protocol for authenticated key agreement in the asymmetric (public-key) setting. The protocol is based on Diffie-Hellman key agreement and can be modified to work in an arbitrary finite group and, in particular, elliptic curve groups. Two modifications of this protocol are also presented: a one-pass authenticated key agreement protocol suitable for environments where only one entity is on-line, and a three-pass protocol in which key confirmation is additionally provided. Variants of these protocols have been standardized in IEEE P1363 [17], ANSI X9.42 [2], ANSI X9.63 [4] and ISO 15496-3 [18], and are currently under consideration for standardization and by the U.S. government's National Institute for Standards and Technology [30].     

Security of a key agreement protocol based on chaotic maps

Kacorev et al. proposed new public key encryption scheme using chaotic maps. Subsequently, Bergamo et al. has broken Kacorev and Tasev’s encryption scheme and then applied the attack on a key agreement protocol based on Kacorev et al.’s system. In order to address Bergamo et al.’ attack, Xiao et al. proposed a novel key agreement protocol. In this paper, we will present two attacks on Xiao et al.’s key agreement protocol using chaotic maps. Our new attack method is different from the one that Bergamo et al. developed. The proposed attacks work in a way that an adversary can prevent the user and the server from establishing a shared session key even though the adversary cannot get any private information from the user and the server’s communications.     

Efficient Arithmetic on Koblitz Curves

It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation.Koblitz introduced a family of curves which admit especially fast elliptic scalar multiplication. His algorithm was later modified by Meier and Staffelbach. We give an improved version of the algorithm which runs 50 than any previous version. It is based on a new kind of representation of an integer, analogous to certain kinds of binary expansions. We also outline further speedups using precomputation and storage.     

Efficiency and security problems of anonymous key agreement protocol based on chaotic maps

In 2011, Niu-Wang proposed an anonymous key agreement protocol based on chaotic maps in [Niu Y, Wang X. An anonymous key agreement protocol based on chaotic maps. Commun Nonlinear Sci Simulat 2011;16(4):1986-92]. Niu-Wang’s protocol not only achieves session key agreement between a server and a user, but also allows the user to anonymously interact with the server. Nevertheless, this paper points out that Niu-Wang’s protocol has the following efficiency and security problems: (1) The protocol has computational efficiency problem when a trusted third party decrypts the user sending message. (2) The protocol is vulnerable to Denial of Service (DoS) attack based on illegal message modification by an attacker.     

Fast elliptic curve point multiplication based on binary and binary non-adjacent scalar form methods

This article presents two methods for developing algorithms of computing scalar multiplication in groups of points on an elliptic curve over finite fields. Two new effective algorithms have been presented: one of them is based on a binary Non-Adjacent Form of scalar representation and another one on a binary of scalar representation method. All algorithms were developed based on simple and composite operations with point and also based on affine and Jacobi coordinates systems taking into account the latest achievements in computing cost reduction. Theorems concerning their computational complexity are formulated and proved for these new algorithms. In the end of this article comparative analysis of both new algorithms among themselves and previously known algorithms are represented.     

椭圆曲线密码的快速算法

80年代,椭圆曲线理论被引入数据加密领域,形成了一种新的公开密钥体制即椭圆曲线密码体制(ECC).该体制中,最耗时的运算是倍点运算也就是椭圆曲线上的点与一个整数的乘法运算.因此倍点运算的快速计算是椭圆曲线密码快速实现的关键.本文提出一种计算kP新的算法,使效率提高38%以上.     

An efficient and secure Diffie–Hellman key agreement protocol based on Chebyshev chaotic map

This paper proposes a new efficient and secure Diffie–Hellman key agreement protocol based on Chebyshev chaotic map. The proposed key agreement protocol uses the semi-group property of Chebyshev polynomials to agree Diffie–Hellman based session key. The proposed protocol provides strong security compared with the previous related protocols. In addition, the proposed protocol does not require any timestamp information and greatly reduces computational costs between communication parties. As a result, the proposed protocol is more practical and provides computational/communicational efficiency compare with several previously proposed key agreement protocols based on Chebyshev chaotic map.     

Avoiding Side-Channel Attacks by Computing Isogenous and Isomorphic Elliptic Curves

Smart cards are being attacked increasingly more, due to their numerous uses and the valuable information stored inside. For this reason, efficient and secure cryptosystems need to be designed. The main problem is that smart cards are resource constrained. Moreover, they are vulnerable to side-channel attacks. In this paper, we use an algorithm to compute side-channel-resistant alternatives to the curves given in the NIST standard and to the new elliptic curves recently presented by Microsoft Research. The algorithm does this by computing isogenous and isomorphic elliptic curves.     

An improved key agreement protocol based on chaos

Cryptography based on chaos theory has developed fast in the past few years, but most of the researches focus on secret key cryptography. There are few public key encryption algorithms and cryptographic protocols based on chaos, which are also of great importance for network security. We introduce an enhanced key agreement protocol based on Chebyshev chaotic map. Utilizing the semi-group property of Chebyshev polynomials, the proposed key exchange algorithm works like Diffie–Hellman algorithm. The improved protocol overcomes the drawbacks of several previously proposed chaotic key agreement protocols. Both analytical and experimental results show that it is effective and secure.     

An anonymous key agreement protocol based on chaotic maps

Recently, Tseng et al. proposed a novel key agreement protocol based on chaotic maps. They claimed that the protocol achieved session key agreement between a server and a user, and allowed the user to anonymously interact with the server. This paper, however, will demonstrate that Tseng et al.’s protocol can not guarantee user anonymity and protocol security against an insider adversary who is a legal user, and it can not provide perfect forward secrecy. Furthermore, the current paper presents a new key agreement protocol based on Chebyshev chaotic map in order to conquer these problems. In contrast with Tseng et al.’s protocol, the proposed protocol is more secure and preserves user anonymity.     

A Formal Language for Cryptographic Protocol Requirements

In this paper we present a formal language for specifying and reasoning about cryptographic protocol requirements. We give sets of requirements for key distribution protocols and for key agreement protocols in that language. We look at a key agreement protocol due to Aziz and Diffie that might meet those requirements and show how to specify it in the language of the NRL Protocol Analyzer. We also show how to map our formal requirements to the language of the NRL Protocol Analyzer and use the Analyzer to show that the protocol meets those requirements. In other words, we use the Analyzer to assess the validity of the formulae that make up the requirements in models of the protocol. Our analysis reveals an implicit assumption about implementations of the protocol and reveals subtleties in the kinds of requirements one might specify for similar protocols.     

Identifying attributes and insecurity of a public-channel key exchange protocol using chaos synchronization

Klein et al. proposed a key exchange protocol using chaos synchronization. The first protocol comprises two parties with chaotic dynamics that are mutually coupled and undergo a synchronization process, at the end of which they can use their identical dynamical state as an encryption key. From cryptographic point of view, their key exchange protocol is a key agreement protocol. Klein et al. claimed that their key agreement can be carried out over a public channel. In order to increase the key space and decrease the precision of the calculation, they made an extension of the system to a network of N Lorenz equations. In this paper, we will provide a cryptanalysis of their key agreement protocol. We will first point out some weaknesses, and then show that their protocol is not secure against several attacks including impersonation attack.     

Efficient password authenticated key agreement using bilinear pairings

For providing a secure distributed computer environment, efficient and flexible user authentication and key agreement is very important. In addition to user authentication and key agreement, identity privacy is very useful for users. In this paper, we propose an efficient and flexible password authenticated key agreement scheme using bilinear pairings. The main merits include: (1) there is no need for any password or verification table in the server; (2) users can choose or change his own password freely; (3) both the server and a user can authenticate each other; (4) it can protect the user’s privacy; (5) the user and the server can generate a session key; (6) it does not have a serious synchronization-clock problem; (7) even if the secret information stored in a smart card is compromised, it can prevent the offline dictionary attack.     

Three-Selmer groups for elliptic curves with 3-torsion

We consider a specific family of elliptic curves with rational 3-torsion subgroup. We arithmetically define 3-Selmer groups through isogeny and 3-descent maps, then associate the image of the 3-descent maps to solutions of homogeneous cubic polynomials affiliated with the elliptic curve E and an isogenous curve E′. Thanks to the work of Cohen and Pazuki, we have solubility conditions for the homogeneous polynomials. Using these conditions, we give a graphical approach to computing the size of 3-Selmer groups. Finally, we translate the conditions on graphs into a question concerning ranks of matrices and give an upper bound for the rank of the elliptic curve E by calculating the size of the Selmer groups.     

Trading Inversions for Multiplications in Elliptic Curve Cryptography

Recently, Eisenträger et al. proposed a very elegant method for speeding up scalar multiplication on elliptic curves. Their method relies on improved formulas for evaluating S=(2P + Q) from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulas save a field multiplication each time the operation is performed. This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling a point, and present a ternary/binary method to perform efficient scalar multiplication.     

Chaotic dynamics of homogeneous Yang-Mills fields with two degrees of freedom

In the present paper, we consider a scenario of transition to chaotic dynamics in the Hamiltonian system of homogeneous Yang-Mills fields with two degrees of freedom in the case of the Higgs mechanism. We show that in such a system, as well as in other Hamiltonian and conservative systems of equations, the nonlocal effect of multiplication of hyperbolic and elliptic cycles and tori around elliptic cycles in neighborhoods of the separatrix surfaces of hyperbolic cycles plays a key role on the initial stage of transition from a regular motion to a chaotic one. We observe that the new elliptic and hyperbolic cycles of the Hamiltonian system are generated as stable and saddle cycles of the extended dissipative system of equations not only as a result of saddle-node bifurcations but also as a result of fork-type bifurcations.     

Strengthening the security of authenticated key exchange against bad randomness

Recent history has revealed that many random number generators (RNGs) used in cryptographic algorithms and protocols were not providing appropriate randomness, either by accident or on purpose. Subsequently, researchers have proposed new algorithms and protocols that are less dependent on the RNG. One exception is that all prominent authenticated key exchange (AKE) protocols are insecure given bad randomness, even when using good long-term keying material. We analyse the security of AKE protocols in the presence of adversaries that can perform attacks based on chosen randomness, i.e., attacks in which the adversary controls the randomness used in protocol sessions. We propose novel stateful protocols, which modify memory shared among a user’s sessions, and show in what sense they are secure against this worst case randomness failure. We develop a stronger security notion for AKE protocols that captures the security that we can achieve under such failures, and prove that our main protocol is correct in this model. Our protocols make substantially weaker assumptions on the RNG than existing protocols.     

Authentication and authenticated key exchanges

We discuss two-party mutual authentication protocols providing authenticated key exchange, focusing on those using asymmetric techniques. A simple, efficient protocol referred to as the station-to-station (STS) protocol is introduced, examined in detail, and considered in relation to existing protocols. The definition of a secure protocol is considered, and desirable characteristics of secure protocols are discussed.This work was done while Whitfield Diffie was with Northern Telecom, Mountain View, California.     

Cryptanalyzing an improved security modulated chaotic encryption scheme using ciphertext absolute value

This paper describes the security weakness of a recently proposed improved chaotic encryption method based on the modulation of a signal generated by a chaotic system with an appropriately chosen scalar signal. The aim of the improvement is to avoid the breaking of chaotic encryption schemes by means of the return map attack introduced by Pérez and Cerdeira. A method of attack based on taking the absolute value of the ciphertext is presented, that allows for the cancellation of the modulation scalar signal and the determination of some system parameters that play the role of system key. The proposed improved method is shown to be compromised without any knowledge of the chaotic system parameter values and even without knowing the transmitter structure.