A New Class of Invertible Mappings
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
A new class of single cycle t-functions
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
Analysis of designing interleaved ZCZ sequence families
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Linear Properties in T-Functions
IEEE Transactions on Information Theory
Permutation Polynomials Modulo 2w
Finite Fields and Their Applications
Linear weaknesses in t-functions
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
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Polynomial functions are widely used in the design of cryptographic transformations such as block ciphers, hash functions and stream ciphers, which belong to the category of T-functions. When a polynomial function is used as state transition function in a pseudorandom generator, it is usually required that the polynomial function generates a single cycle. In this paper, we first present another proof of the sufficient and necessary condition on a polynomial function $f(\mathbf{x})=c_0+c_1\mathbf{x}+c_2\mathbf{x}^2+\cdots+c_m\mathbf{x}^m \bmod 2^n(n \geq 3)$ being a single cycle T-function. Then we give a general linear equation on the sequences {xi} generated by these T-functions, that is, $$ \mathbf{x}_{i+2^{j-1},j}=\mathbf{x}_{i,j}+\mathbf{x}_{i,j-1} +ajA_{i,2}+a(j-1)+b\bmod 2,3\leq j \leq n-1, $$where Ai,2is a sequence of period 4, aand bare constants determined by the coefficients ci. This equation shows that the sequences generated by polynomial single cycle T-functions have potential secure problems.