Safer parameters for the Chor–Rivest cryptosystem

AbstractVaudenay’s cryptanalysis against Chor–Rivest cryptosystem is applicable when the parameters, p and h, originally proposed by the authors are used. Nevertheless, if p and h are both prime integers, then Vaudenay’s attack is not applicable. In this work, a choice of these parameters resistant to the existing cryptanalytic attacks, is presented. The parameters are determined in a suitable range guaranteeing its security and the computational feasibility of implementation. Regrettably, the obtained parameters are scarce in practice

An Implementation of the Chor-Rivest Knapsack Type Public Key Cryptosystem

The Chor-Rivest cryptosystem is a public key cryptosystem first proposed by MIT cryptographers Ben Zion Chor and Ronald Rivest [Chor84]. More recently Chor has imple mented the cryptosystem as part of his doctoral thesis [Chor85]. Derived from the knapsack problem, this cryptosystem differs from earlier knapsack public key systems in that computa tions to create the knapsack are done over finite algebraic fields. An interesting result of Bose and Chowla supplies a method of constructing higher densities than previously attain able [Bose62]. Not only does an increased information rate arise, but the new system so far is immune to the low density attacks levied against its predecessors, notably those of Lagarias- Odlyzko and Radziszowski-Kreher [Laga85, Radz86]. An implementation of this cryptosystem is really an instance of the general scheme, dis tinguished by fixing a pair of parameters, p and h , at the outset. These parameters then remain constant throughout the life of the implementation (which supports a community of users). Chor has implemented one such instance of his cryptosystem, where p =197 and h =24. This thesis aspires to extend Chor\u27s work by admitting p and h as variable inputs at run time. In so doing, a cryptanalyst is afforded the means to mimic the action of arbitrary implementations. A high degree of success has been achieved with respect to this goal. There are only a few restrictions on the choice of parameters that may be selected. Unfortunately this general ity incurs a high cost in efficiency; up to thirty hours of (VAX1 1-780) processor time are needed to generate a single key pair in the desired range (p = 243 and h =18)

Quadratic compact knapsack public-key cryptosystem

AbstractKnapsack-type cryptosystems were among the first public-key cryptographic schemes to be invented. Their NP-completeness nature and the high speed in encryption/decryption made them very attractive. However, these cryptosystems were shown to be vulnerable to the low-density subset-sum attacks or some key-recovery attacks. In this paper, additive knapsack-type public-key cryptography is reconsidered. We propose a knapsack-type public-key cryptosystem by introducing an easy quadratic compact knapsack problem. The system uses the Chinese remainder theorem to disguise the easy knapsack sequence. The encryption function of the system is nonlinear about the message vector. Under the relinearization attack model, the system enjoys a high density. We show that the knapsack cryptosystem is secure against the low-density subset-sum attacks by observing that the underlying compact knapsack problem has exponentially many solutions. It is shown that the proposed cryptosystem is also secure against some brute-force attacks and some known key-recovery attacks including the simultaneous Diophantine approximation attack and the orthogonal lattice attack

Genetic algorithms in cryptography

Genetic algorithms (GAs) are a class of optimization algorithms. GAs attempt to solve problems through modeling a simplified version of genetic processes. There are many problems for which a GA approach is useful. It is, however, undetermined if cryptanalysis is such a problem. Therefore, this work explores the use of GAs in cryptography. Both traditional cryptanalysis and GA-based methods are implemented in software. The results are then compared using the metrics of elapsed time and percentage of successful decryptions. A determination is made for each cipher under consideration as to the validity of the GA-based approaches found in the literature. In general, these GA-based approaches are typical of the field. Of the genetic algorithm attacks found in the literature, totaling twelve, seven were re-implemented. Of these seven, only three achieved any success. The successful attacks were those on the transposition and permutation ciphers by Matthews [20], Clark [4], and Griindlingh and Van Vuuren [13], respectively. These attacks were further investigated in an attempt to improve or extend their success. Unfortunately, this attempt was unsuccessful, as was the attempt to apply the Clark [4] attack to the monoalphabetic substitution cipher and achieve the same or indeed any level of success. Overall, the standard fitness equation genetic algorithm approach, and the scoreboard variant thereof, are not worth the extra effort involved. Traditional cryptanalysis methods are more successful, and easier to implement. While a traditional method takes more time, a faster unsuccessful attack is worthless. The failure of the genetic algorithm approach indicates that supplementary research into traditional cryptanalysis methods may be more useful and valuable than additional modification of GA-based approaches

A Comparison between Memetic algorithm and Genetic algorithm for the cryptanalysis of Simplified Data Encryption Standard algorithm

Genetic algorithms are a population-based Meta heuristics. They have been successfully applied to many optimization problems. However, premature convergence is an inherent characteristic of such classical genetic algorithms that makes them incapable of searching numerous solutions of the problem domain. A memetic algorithm is an extension of the traditional genetic algorithm. It uses a local search technique to reduce the likelihood of the premature convergence. The cryptanalysis of simplified data encryption standard can be formulated as NP-Hard combinatorial problem. In this paper, a comparison between memetic algorithm and genetic algorithm were made in order to investigate the performance for the cryptanalysis on simplified data encryption standard problems(SDES). The methods were tested and various experimental results show that memetic algorithm performs better than the genetic algorithms for such type of NP-Hard combinatorial problem. This paper represents our first effort toward efficient memetic algorithm for the cryptanalysis of SDES.Comment: 9Page