Cryptology ePrint Archive: Report 2009/416

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

Carsten Elsner and Martin Schmidt

Abstract: 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.

Category / Keywords: secret-key cryptography / block ciphers, number theory, diophantine analysis

Date: received 26 Aug 2009

Contact author: mschmidt at ifam uni-hannover de

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Version: 20090901:065504 (All versions of this report)

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