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 cryptosystems, 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 large integers, a problem that is solved in polynomial time by Shor's algorithm.

References

  1. ↑ Shamir 1982.
  2. ↑ Adleman 1982.
  3. ↑ Nasako & Murikami 2006.

Bibliography

  • Leonard Adleman (1982), "On breaking the titrated Merkle-Hellman public-key cryptosystem", Crypto'82, Springer: 303–308, doi:10.1007/978-1-4757-0602-4_29
  • Adi Shamir (1982), "A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystems", FOCS'82, IEEE, doi:10.1109/SFCS.1982.5
  • T. Nasako; Y. Murakami (2006), "A high-density knapsack cryptosystem using combined trapdoor", Japan Society for Industrial and Applied Mathematics, 16 (4): 519–605
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