Southwest Jiaotong University School of Mathematics


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On Ideal t-Tuple Distribution of Orthogonal Functions in Filtering de Bruijn Generators

报告内容:Uniformity of binary tuples of various lengths in a pseudorandom sequence is an important randomness property for cryptographic applications. We consider the problem how to convert a uniformly distributed binary tuples of length n in a pseudorandom sequence into another a pseudorandom sequence with uniformly distributed binary tuples through filtering models.  

In general, not any filtering function can be used to achieve uniformity in binary tuples.  

We restrict ourselves to the family of orthogonal functions, i.e., those correspond to binary sequences with ideal 2-level autocorrelation, which are also a rich source for known APN functions and almost bent functions. It is known that if we apply the so-called WG transform to the known orthogonal functions, then there is only one class whose orthogonality remains, called WG-sequences.  This result is first conjectured in 1997, proved by Dillon for odd n and Dillon and Dobbertin in 2004 for even $n$.   WG transformation and WG sequences have been used in WG stream cipher, which is to filter over a linear feedback shift register sequence.  After the twenty years of discovering WG transformations, there is no much more significant results on randomness on WG transformation sequences reported. In this talk, I will present our new results on uniformity of WG transformation as filtering functions on de Bruijn sequences.  Surprisingly, we have found that there are only two classes of orthogonal functions whose WG transformations will reserve some uniformity of the output sequences, where one is obtained by decimation from the original WG transformation and the other class is obtained by decimation from WG   for transformation over 3-term sequences, the later does not have 2-level autocorrelation.  

报告人简介:Guang Gong,  B.S(1981)-M.S (1985)-Ph.D (1990),  has been a full Professor since 2004, in the department of Electrical and Computer Engineering, University of Waterloo. Dr. Gong’s research interests are in the areas of  pseudorandom sequences, cryptography  and communication security. She has authored or co-authored more than 350 technical papers;   two books,  Signal Design for Good Correlation for Wireless Communication, Cryptography and Radar (2005), co-authored with Dr. Golomb, Communication System Security (2012), coauthored with Dr. Lidong Chen; and two patents.   Dr. Gong’s research has received the supports from government funding agencies including federal grant agency NSERC, provincial grant ORF in Canada, NIST (US), and a number of industrial partners.  Dr. Gong serves/served as Associate Editors for several journals including Associate Editor of IEEE Transactions on Information Theorem (IT) (2005-2008) and IEEE IT Special Issue on Shift-?Register Sequences, Codes and Cryptography in Memory of Solomon W. Golomb (2017-2018), the journal of Cryptography and Communications (2007-),  and serves/served on numerous technical program committees  as co-chairs/organizers or committee members.  She is an IEEE Fellow 2014 and   University Research Professor 2018.

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