An augmented family of cryptographic Parity Circuits
A computationally inexpensive involution called value dependent swapping is introduced. This involution is included in the non-linear cryptographic family of functions called Parity Circuits to increase its non-affineness and thus increase its strength against cryptanalysis. Our analysis shows that this augmented version of Parity Circuits still has fundamental cryptographic properties. The addition of this involution introduces a new type of randomization while preserving the invertibility of the functions being defined. We formulate affineness for a general function, and introduce a normalized non-affineness measure. We prove some non-affineness conditions for the augmented Parity Circuits, and evaluate their non-affineness. We suggest the value-dependent swapping can also be incorporated into DES-like cryptographic functions as well to make them stronger against cryptanalysis.
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