報(bào)告人：李春雷博士

報(bào)告內(nèi)容：DeBruijn sequences from LFSRs

報(bào)告時(shí)間：2017年11月24日（周五）上午10：00-11：30

報(bào)告地點(diǎn)：X9207

報(bào)告摘要：A binary de Bruijn sequence of order $n$ is a cyclic sequence of period $2^n$, in which each $n$-bit pattern appears exactly once. De Bruijn sequences have important applications in cryptography, communication and coding theory for their desirable characteristics such as long periods, large complexities and good randomness properties. For example, de Bruijn sequences are useful in random number generation, which is essential for secure communication especially for generation of cryptographic keys, nonces and salts; in stream cipher designs, feedback shift registers (FSRs) that can generate de Bruijn sequences are commonly used. All three hardware-oriented Ecrypt eStream competition finalists, namely Trivium, Grain and Mickey use these registers as their main building block. However, the theory of nonlinear FSRs is far less developed and comprehended in comparison with that of linear FSRs). It is well known that the number of unique de Bruijn sequences is equal to $2^{2^{n-1}-n}$, however only a very small number are known to have simple and efficient constructions, and the properties of the constructed sequences are not well understood. This fact would be best captured by a quote in Fredricksen’s excellent survey: ``\textit{When a mathematician on the street is presented with the problem of generating a de Bruijn sequence, one of the three things happens: he gives up, or produces a sequence based on a primitive polynomial, or produces the prefer-one sequence. Only rarely a new algorithm is proposed.}” Fredricksen’s statement might appear a little subjective, unfortunately it turned out to be more or less true in the last 40 years.

Although there wasn’t much development in the research on deBruijn sequences, some constructions of de Bruijn sequences from LFSRs have been proposed in recent years. This talk will introduce recent research progress in this direction.

報(bào)告人簡介：李春雷于2001 至2008 年間在湖北大學(xué)完成數(shù)學(xué)系學(xué)士學(xué)位和密碼學(xué)碩士學(xué)位。在2008 至2014年期間，李春雷先后就讀于武漢大學(xué)，挪威卑爾根大學(xué)，并相應(yīng)取得信息安全專業(yè)博士學(xué)位和可靠通信專業(yè)博士學(xué)位；現(xiàn)就職于卑爾根大學(xué)。在攻讀碩士和博士學(xué)位期間，李春雷在國際知名期刊上發(fā)表高質(zhì)量學(xué)術(shù)論文20 余篇，其中包括在計(jì)算機(jī)學(xué)會(huì)（CCF）建議的A 類期刊IEEE Transaction on Information Theory 上發(fā)表論文6篇。