Abstract
At Eurocrypt2011, Becker, Coron and Joux proposed an algorithm for solving hard knapsacks, i.e., knapsacks with a density close to 1. Their algorithm solves hard knapsacks in time \(\tilde{O}(2^{0.2909n})\). In this paper, we evaluate their algorithm by O notation and prove that the running time is O(n 3.5 ·20.2909n). Furthermore, we extend their algorithm and propose the algorithm of which running time is O(n 3 ·20.2919n). Asymptotic running time of our algorithm is not faster. However, when n < 6312, our algorithm can solve subset sum problem faster than algorithm of Becker, Coron and Joux.
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References
Becker, A., Coron, J.S., Joux, A.: Improved Generic Algorithms for Hard Knapsacks. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 364–385. Springer, Heidelberg (2011)
Coster, M.J., Joux, A., LaMacchia, B.A., Odlyzko, A.M., Schnorr, C.P., Stern, J.: Improved Low-Density Subset Algorithms. Computational Complexity 2, 111–128 (1992)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman (1979)
Howgrave-Graham, N., Joux, A.: New Generic Algorithms for Hard Knapsacks. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 235–256. Springer, Heidelberg (2010)
Lagarias, J.C., Odlyzko, A.M.: Solving Low-Density Subset Sum Problems. Journal of the Association for Computing Machineary 32(1), 229–246 (1985)
Merkle, R.C., Hellman, M.E.: Hiding Information and Signatures in Trapdoor Knapsacks. IEEE Transactions on Information Theory 24, 525–530 (1978)
Schroeppel, R., Shamir, A.: A T = O(2n/2), S = O(2n/4) Algorithm for Certain NP-Complete Problems. SIAM Journal on Computing 10(3), 456–464 (1981)
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Nagashima, Y., Kunihiro, N. (2012). Faster Algorithm for Solving Hard Knapsacks for Moderate Message Length. In: Susilo, W., Mu, Y., Seberry, J. (eds) Information Security and Privacy. ACISP 2012. Lecture Notes in Computer Science, vol 7372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31448-3_4
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DOI: https://doi.org/10.1007/978-3-642-31448-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31447-6
Online ISBN: 978-3-642-31448-3
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