When doing cryptanalysis on RSA or something number theory based, there are various attacks that all seem to involve number theory (Wikipedia: RSA_(algorithm) ~ Attacks_against_plain_RSA). Similarly, attacks on ECC seem to involve something from ECC (Elliptic curve cryptography related key attacks).

What I'm wondering about is matrix-based (perhaps someone can correct me to the proper term for this) cryptography and cryptanalysis. I'm especially wondering if I'm just stating the obvious by associating the attacks with their original crypto-systems or if there are methods that work for different kinds of systems based on different math theory (an example of this would really be helpful). Particularly the matrix-based (which seems to involve multiple points orthogonal in $R^n$).

Can cryptanalysis based on that be used on other crypto-systems?

  • $\begingroup$ what do you mean by matrix based cryptography? $\endgroup$ – CodesInChaos Oct 17 '13 at 7:20
  • $\begingroup$ I was trying to find the right term. It's the use of matrices and linear algebra in cryptography. Very large matrices are applied like this en.wikipedia.org/wiki/Hill_cipher or like this aix1.uottawa.ca/~jkhoury/cryptography.htm but as I said I'm not sure how to categorize it. $\endgroup$ – stackuser Oct 17 '13 at 14:05
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    $\begingroup$ In the wiki article you linked the problem for the Hill cipher is stated clearly, and it is true for similar problems: Linear systems are fairly easy to break with known plaintext attacks and even easier with chosen plaintext attacks. In syemmtric encryption, S boxes are designed to be as non-linear as possible while keeping some additional properties like being uniform distributed, etc. But there are applications of matrixes in cryptography: Lattice-based crypto uses them extensively, and the McEliece cryptosystem is based on linear codes and large matrices. $\endgroup$ – tylo Oct 17 '13 at 14:37