Paper 2009/416

KronCrypt - A New Symmetric Cryptosystem Based on Kronecker's Approximation Theorem

Carsten Elsner and Martin Schmidt


In this paper we show how to use an old mathematical concept of diophantine analysis, the approximation theorem of Kronecker, in symmetric cryptography. As a first practical application we propose and analyze the new symmetric 128-bit block cipher KronCrypt. The cipher is a 4-round Feistel network with a non-bijective round function f made up of a variable number of large key-dependent S-boxes, XORs and modular additions. Its key length is variable but not less than 128 bit. The main innovation of KronCrypt in the area of symmetric cryptography is the fact that the key-dependent S-boxes are based upon a constructive proof of the approximation theorem of Kronecker used as a boolean function. We prove the correctness of our concept in general and show how we designe the new cipher KronCrypt. Furthermore, results concerning statistical behaviour, i.e. confusion, diffusion and completeness, and differential cryptanalysis are presented.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
block ciphersnumber theorydiophantine analysis
Contact author(s)
mschmidt @ ifam uni-hannover de
2009-09-01: received
Short URL
Creative Commons Attribution


      author = {Carsten Elsner and Martin Schmidt},
      title = {KronCrypt - A New Symmetric Cryptosystem Based on Kronecker's Approximation Theorem},
      howpublished = {Cryptology ePrint Archive, Paper 2009/416},
      year = {2009},
      note = {\url{}},
      url = {}
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