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- W1586151034 abstract "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 $f(mathbf{x})=c_0+c_1mathbf{x}+c_2mathbf{x}^2+cdots+c_mmathbf{x}^m bmod 2^n(n geq 3)$ being a single cycle T-function. Then we give a general linear equation on the sequences { x i } generated by these T-functions, that is, $$ mathbf{x}_{i+2^{j-1},j}=mathbf{x}_{i,j}+mathbf{x}_{i,j-1} +ajA_{i,2}+a(j-1)+bbmod 2,3leq j leq n-1, $$ where A i,2 is a sequence of period 4, aand bare constants determined by the coefficients c i . This equation shows that the sequences generated by polynomial single cycle T-functions have potential secure problems." @default.
- W1586151034 created "2016-06-24" @default.
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- W1586151034 date "2008-08-16" @default.
- W1586151034 modified "2023-09-27" @default.
- W1586151034 title "Linear Equation on Polynomial Single Cycle T-Functions" @default.
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- W1586151034 doi "https://doi.org/10.1007/978-3-540-79499-8_21" @default.
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