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On Algebraic Property of T-Functions
Ruilin LI Bing SUN Chao LI Shaojing FU
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2012/01/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Cryptography and Information Security)
cryptographic functions, single-cycle T-function, modular addition, algebraic degree,
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T-function is a kind of cryptographic function which is shown to be useful in various applications. It is known that any function f on F2n or Z2n automatically deduces a unique polynomial fF ∈ F2n[x] with degree ≤ 2n-1. In this letter, we study an algebraic property of fF while f is a T-function. We prove that for a single cycle T-function f on F2n or Z2n, deg fF=2n-2 which is optimal for a permutation. We also consider a kind of widely used T-function in many cryptographic algorithms, namely the modular addition function Ab(x)=x+b ∈ Z2n[x]. We demonstrate how to calculate deg Ab F from the constant value b. These results can facilitate us to evaluate the immunity of the T-function based cryptosystem against some known attacks such as interpolation attack and integral attack.