Solving low-density subset sum problems
Journal of the ACM (JACM)
A knapsack type public key cryptosystem based on arithmetic in finite fields
Proceedings of CRYPTO 84 on Advances in cryptology
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
New definition of density on knapsack cryptosystems
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Adapting density attacks to low-weight knapsacks
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
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The density is a very important parameter in knapsack public-key cryptosystems. It is known that the knapsack cryptosystem is broken with the low-density attack when the density is low. In 2005, Nguyen and Stern introduced the pseudo-density instead of the conventional density in order to evaluate CR and OTU cryptosystems. In 2008, Kunihiro introduced a new density in order to unify the conventional density and the pseudo-density. From Kunihiro's result, we can guess that the plaintext is disclosed with the low-density attack when the weight of the plaintext is low even in the conventional knapsack PKC. In this paper, we investigate the relationship between the weight of plaintext and successful attacks in conventional knapsack cryptosystems.