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# New Constructions of T-function

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9065)

## Abstract

T-function is a mapping from a Boolean matrix to a Boolean matrix with the property that i-th column of the output matrix depends on the first i columns of the input matrix. In 2003, Klimov and Shamir first introduced the concept of T-function. Using T-function we can construct some invertible functions which can be used to construct block cipher. Some invertible and full cycle T-functions can be used to construct stream cipher. Inversion procedure of these functions are different from the normal invertible functions and which is also hard. In 2005, Hong et al. constructed new class of full cycle T-function. In their construction the i-th column of the output matrix actually depends only on the i-th column of the input matrix. Our construction is more general than Hong et al’s construction with good cryptographic properties. In this paper, we present a new construction of T-function. We study the invertibility, cycle length and nonlinearity of this T-function. Furthermore, we construct a new full cycle T-function. Invertible and highly nonlinear functions can be used to design block cipher. Full cycle functions can be used in LFSR based stream cipher to get the full period of the stream cipher in place of linear state update function.

## Keywords

T-function Boolean function cycle length nonlinearity permutations

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## References

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## Copyright information

© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• Dibyendu Roy
• 1
Email author
• Ankita Chaturvedi
• 1
• Sourav Mukhopadhyay
• 1
1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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