报告题目：The non-Archimedean theory of T-functions, with application to cryptology

报告人：V. Anashin教授(莫斯科大学数学系)

时间：2012年11月8日（星期四）16:00-17:00

地点：理科楼数学系A304

摘要:A T-function is a "triangular-shaped" map from n-bit words to n-bit words, i.e., such that the i-th position bit of image does not depend of bits in positions i,i+1,...,n-1 of the pre-image, i=0,1,2,...,n-1. Typical examples of T-functions are computer instructions, both numerical (such as integer addition, integer multiplication, etc.) and bitwise logical (such as xor, bitwise exclusive or, bitwise and, etc.) as well as their arbitrary compositions.The T-functions can be regarded as straight-line programs of computers and that is why they are used in modern cryptographic primitives. A T-function on n-bit words can naturally and uniquelly be extended to the function on infinite binary words. Once the latter words are regarded as 2-adic integers, the T-functions are 1-Lipschitz (whence,continuous)2-adically valued functions on the metric space of 2-adic integers. In the lecture, there will be given an overview of methods of 2-adic analysis and of 2-adic ergodic theory in a study of various cryptographic properties of T-functions.

联系人：姚家燕