Theory and Application of Algebraic Feedback Shift Registers

代数反馈移位寄存器的理论与应用首席研究员：Andrew Klapper，肯塔基大学（University of kentucky）数字通信与信息技术中必不可少的随机序列。它们用于流密码密码系统；在蜂窝电话、GPS系统和卫星通信的扩频系统中；也可以作为数字通信纠错码中的码字。大数的伪随机序列用于大型模拟，如天气预报、反应堆设计、油井勘探、放射癌症治疗、交通流量和金融工具定价等应用。在每种情况下，都需要具有特定属性的序列。然而，很少有有效生成伪随机序列的通用方法。本研究涉及开发和分析大量伪随机序列，用于密码学、编码理论和模拟中的各种应用。解析：选A。Klapper和M. Goresky提出了“进位反馈移位寄存器”（FCSRs），这是一类易于实现的伪随机生成器，它可以快速生成具有许多理想性质的伪随机序列。这些后来被推广到代数反馈移位寄存器（afsr）。FCSRs和AFSRs的许多基本性质已经确定。本项目研究FCSR和AFSR序列的相关问题，包括：(1)设计用于生成密码安全序列的“组合器”、“前馈函数”和时钟控制电路，(2)设计用于准蒙特卡罗（QMC）的具有良好统计特性的快速高效的FCSR，(3)分析和设计几种新的AFSR生成器，应用于流密码和QMC，(4)解决AFSR的寄存器合成问题。(5)基于afsr序列的纠错块码和卷积码新家族的开发。

Theory and Application of Algebraic Feedback Shift RegistersPrincipal Investigator: Andrew Klapper, University of KentuckyPseudorandom sequences essential for digital communications and information technology. They are used in stream cipher cryptosystems; in spread spectrum systems in cellular telephones, GPS systems, and satellitecommunications; and as codewords in error-correcting codes for digital communication. Pseudorandom sequences of large numbers are used in large simulations for such applications as weather prediction, reactor design, oil well exploration, radiation cancer therapy, traffic flow, and pricing of financial instruments. In each case sequences with particular properties are needed. Yet few general methods for efficient generation of pseudorandom sequences are known. This research involves the development and analysis of a large supply of pseudorandom sequences for a variety of applications in cryptography, coding theory, and simulations.In 1994 A. Klapper and M. Goresky proposed "feedback-with-carry shift registers" (FCSRs), a class of pseudorandom generators which are easily implemented and which rapidly generate pseudorandom sequences with many desirable properties. These were later generalized to algebraic feedback shift registers (AFSRs). Many basic properties of FCSRs and AFSRs have been determined. This project addresses issues concerning FCSR and AFSR sequences including (1) design of "combiners", "feedforward functions", and clock-controlled circuits for the generation of cryptographically secure sequences, (2) design of fast and efficient FCSRs with good statistical properties for use in quasi-Monte Carlo (QMC), (3) analysis and design of several new AFSR generators with applications to stream ciphers and QMC, (4) solution of the register synthesis problem for AFSRs, and (5) development of new families of error correcting block and convolutional codes based onAFSR sequences.