Knapsack cryptosystems

Knapsack Cryptosystems are cryptosystems which security is based on the hardness of solving the knapsack problem. While such systems have been existing for quite a long time, they remain quite unpopular because a lot of such systems have been broken. However that type of cryptosystem is a good candidate for post-quantum cryptography

The most famous knapsack cryptosystem is the Merkle-Hellman Public Key Cryptosystem, one of the first public key cryptosystem, published the same year as the RSA cryptosystem. However this system has been broken by several attacks : one from Shamir,[1] one by Adleman,[2] and the low density attack.

However there exist modern knapsack cryptosystems that are considered secure so far : among them is Nasako-Murakami 2006.[3]

What is interesting with those systems is that the Knapsack problem, in the settings where no attack were found, is believed to be difficult to solve even by a quantum computer. This is not the case for systems as RSA relying on the problem of factoring big integers, a problem that is solved in linear time by Shor's quantum algorithm.

References

  1. ↑ A. Shamir, A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystems, Proc. Crypto’82, LNCS, pp.279–288, Springer-Verlag, Berlin, 1982.
  2. ↑ L. M. Adleman, On breaking the titrated Merkle-Hellman public-key cryptosystem, Plenum Press. Crypto’82, pp.303–308. 1982.
  3. ↑ T. Nasako and Y. Murakami, A high-density knapsack cryptosystem using combined trapdoor, the Japan Society for Industrial and Applied Mathematics, Vol.16, No.4, pp.519-605, 2006.
This article is issued from Wikipedia - version of the Thursday, July 24, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.