Cryptanalytic Results on Knapsack Cryptosystem Using Binary Particle Swarm Optimization

The security of most Public Key Cryptosystem (PKC) proposed in literature relies on the difficulty of the integer factorization problem or discrete logarithm problem. However, using shor’s [19] algorithm the problems can be solved in acceptable amount of time via ‘quantum computers’. Therefore in this context knapsack (more accurately subset sum problem(SSP)) based PKC is reconsidered as a viable option by the cryptography community. However, before considering the practicability of this cryptosystem, there is a growing need to cryptanalyze it using all possible present techniques, in order to guarantee their security. We believe that modern Computation Intelligence (CI) techniques can provide efficient cryptanalytic results (because of the new aspects have been incorporated in CI techniques). In this paper, we use two different binary particle swarm optimization techniques to cryptanalyze knapsack PKC. The results obtained via extensive testing are promising and proficient. We present, discuss and compare the effectiveness of the proposed work in the result section.

[1]  Ian Goldberg,et al.  Generalizing cryptosystems based on the subset sum problem , 2011, International Journal of Information Security.

[2]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[3]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[4]  M. Danziger,et al.  Computational Intelligence Applied on Cryptology: a brief review , 2012, IEEE Latin America Transactions.

[5]  David W. Pyle Intelligence: an Introduction , 1979 .

[6]  Martin E. Hellman,et al.  Hiding information and signatures in trapdoor knapsacks , 1978, IEEE Trans. Inf. Theory.

[7]  Jar-Ferr Yang,et al.  Knapsack Cryptosystems and Unreliable Reliance on Density , 2012, 2012 IEEE 26th International Conference on Advanced Information Networking and Applications.

[8]  Masao Kasahara,et al.  A public-key cryptosystem based on decision version of subset sum problem , 2012, 2012 International Symposium on Information Theory and its Applications.

[9]  Antoine Joux,et al.  Improved low-density subset sum algorithms , 1992, computational complexity.

[10]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[11]  Gil Segev,et al.  Public-Key Cryptographic Primitives Provably as Secure as Subset Sum , 2010, TCC.

[12]  Richard Spillman,et al.  Cryptanalysis of Knapsack Ciphers Using Genetic Algorithms , 1993, Cryptologia.

[13]  Álvaro Herrero,et al.  A Neural-Visualization IDS for Honeynet Data , 2012, Int. J. Neural Syst..

[14]  Vicente Julián,et al.  RT-MOVICAB-IDS: Addressing real-time intrusion detection , 2013, Future Gener. Comput. Syst..

[15]  Adi Shamir,et al.  A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[16]  Jeffrey C. Lagarias,et al.  Solving low density subset sum problems , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[17]  Yehuda Lindell,et al.  More Efficient Constant-Round Multi-Party Computation from BMR and SHE , 2016, IACR Cryptol. ePrint Arch..

[18]  Poonam Garg,et al.  An Enhanced Cryptanalytic Attack on Knapsack Cipher using Genetic Algorithm , 2007 .

[19]  Yupu Hu,et al.  Quadratic compact knapsack public-key cryptosystem , 2010, Comput. Math. Appl..

[20]  Andries P. Engelbrecht,et al.  Computational Intelligence: An Introduction , 2002 .

[21]  M. Kasahara,et al.  A new class of cryptosystems based on Chinese remainder theorem , 2008, 2008 International Symposium on Information Theory and Its Applications.

[22]  Yupu Hu,et al.  A knapsack-based probabilistic encryption scheme , 2007, Inf. Sci..

[23]  Kusum Deep,et al.  A Modified Binary Particle Swarm Optimization for Knapsack Problems , 2012, Appl. Math. Comput..