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Virtual Isomorphisms of Ciphers: Is AES Secure Against Differential / Linear Attack?

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Executive Summary

Cipher is vulnerable to an attack if isomorphic cipher is vulnerable to this attack. That method is based on conjugation, and it is not practical because all round operations except one become nonlinear. New isomorphism of AES is proposed, its image IAES has only one nonlinear operation IXOR - isomorphic image of XOR of 5 bytes. Maximal probabilities of byte differentials are increased about 10-11 times, maximal biases of linear sums are increased about 3.6 times comparatively to original AES. IAES possesses computable family of differentials of IXOR with two active input bytes, zero output difference and probability 1. Zero output difference decreases the rate of multiplication of active nonlinearities in differential characteristic of IAES.

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