Trace Representations of S-boxes and Their Application

In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functionsF(x)=x d over field GF(2 n ), withW(d)=n?1, have desirable cryptographic properties. Therefore we generalize an important result of Nyberg. As application, we use these conclusions to analyze cryptographic property of the S-box of AES (the Advanced Encryption Standard) and give its several equivalent representations, proving that the composition of inversion function of AES and any invertible affine transformations is impossible to satisfy strict avalanche criterion, any order propagation criteria and any order correlation immunity. Key words trace function - nonlinearity - differentially uniform - strict avalanche criterion CLC number TP 309 Foundation item: Supported by the National Natural Science Foundation of China (60373089, 60373041), Natural Science Foundation of Hubei Province (2002AB0037) and Chen-guang Plan of Wuhan City (20025001007).Biography: Zeng Xiang-yong (1973-), male, A postdoctoral fellow, research direction: cryptology and the representation theory of algebra.

On Algebraic Immunity of Trace Inverse Functions on Finite Fields of Characteristic Two

The trace inverse functions Tr(λx^(-1)) over the finite field F_(2~n) are a class of very important Boolean functions and are used in many stream ciphers such as SFINKS,RAKAPOSHI,the simple counter stream cipher(SCSC) presented by Si W and Ding C(2012),etc.In order to evaluate the security of those ciphers in resistance to(fast) algebraic attacks,the authors need to characterize algebraic properties of Tr(λx^(-1)).However,currently only some bounds on algebraic immunity of Tr(λx^(-1)) are given in the public literature,for example,the NGG upper bound and the Bayev lower bound,etc.This paper gives the exact value of the algebraic immunity of Tr(λx^(-1)) over F_(2~n),that is,AI(Tr(λx^(-1))) =[2n^(1/2)]- 2,where n ≥ 2,A ∈ F_(2~n) and λ≠ 0,which shows that Dalai's conjecture on the algebraic immunity of Tr(λx^(-1)) is correct.What is more,the authors demonstrate some weak properties of Tr(λx^(-1)) against fast algebraic attacks.

THE CHANGES OF PANCREATIC ACINAR CELL FUNCTION IN ACUTE NECROTIZING PANCREATITIS OF RATS

ObjectiFe To evaluate the changes of pancreatic acinar cell functions in the rats with acutenecrotizing pancreatitis (ANP). methods Seventy SD rats were randomized into two groups: experimental group(n=35) and control group (n=35). To prepare the experimental model, the retrograde injection of 5% sodiumtaurocholate into the pancreatic duct was used for inducing ANP. Radioactive tracing by L -3H-phenylalanineand autoradiography were performed for scoring the differences of changes of amino acid uptake, enzyme-proteinsynthesis and output from acinar cells in rats between both groups. Results No changes were observed in aminoacid uptake and enzyme -protein synthesis in rats with dotted and haemorrhagic necrotizing foci as compared withcontrol group. However, accumulated zymogen granules in the interstitial of acinar cells were seen in theexperimental group. Conclusion It indicates that in experimental ANP rats, the functions of acinar cells in bothamino acid uptake and protein synthesis were essentially normal, but the pathway of enzyme output was affectedinto ectopic secretion through the bottom or lateral cellular membrane of pancreatic acinar cell.

The Walsh Transform of a Class of Boolean Functions

The Walsh transform is an important tool to investigate cryptographic properties of Boolean functions.This paper is devoted to study the Walsh transform of a class of Boolean functions defined as g(x)=f(x)Tr^(n)_(1)(x)+h(x)Tr^(n)_(1)(δx),by making use of the known conclusions of Walsh transform and the properties of trace function,and the conclusion is obtained by generalizing an existing result.