Proceedings of CRYPTO 84 on Advances in cryptology
Non-injective knapsack public-key cryptosystems
Theoretical Computer Science
A knapsack-based probabilistic encryption scheme
Information Sciences: an International Journal
Linear Bandwidth Naccache-Stern Encryption
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Cryptanalysis of a knapsack-based probabilistic encryption scheme
Information Sciences: an International Journal
Hiding information and signatures in trapdoor knapsacks
IEEE Transactions on Information Theory
A polynomial-time algorithm for breaking the basic Merkle - Hellman cryptosystem
IEEE Transactions on Information Theory
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Wang et al. [B. Wang, Q. Wu, Y. Hu, Information Sciences 177 (2007)] proposed a knapsack-based probabilistic encryption scheme with non-binary coefficients which enjoys a high density larger than 1.06 in the worst case. In this work, we successfully attack this scheme by showing that a public key and a restriction on system parameters allow the attacker to recover a secret key in a cubic time complexity using modular equations. This approach is much more efficient than the previous attack by Youssef [A.M. Youssef, Information Sciences 179 (2009)], in which lattice basis reductions are used. Recovering secret keys can be done within 4h and 4days when n=100 and 200, respectively. A simple modification that helps resist known attacks is also discussed.