CIF:Small: Primitives for Cryptography and Communications

小型：用于密码学和通信的原语 主要研究者：Andrew Klapper，肯塔基州大学 伪随机序列和高度非线性函数在数字通信和信息技术中是必不可少的。 它们被用于流密码密码系统、蜂窝电话中的扩频系统、GPS系统、卫星通信、数字通信的纠错码，以及天气预测、反应堆设计、油井勘探、放射性癌症治疗、交通流量和金融工具定价等应用的大型模拟。 在每种情况下，需要具有特定性质的序列或非线性函数。 然而，高质量的伪随机序列和高度非线性函数的一般构造是已知的。 这项研究涉及大量供应这些工具的开发和分析，用于密码学，编码理论和模拟中的各种应用。 1994年，Klapper和Goresky提出了“带进位反馈移位寄存器”（FCSR），这是一种易于实现的伪随机发生器，可以快速生成具有许多理想特性的序列。 这些一般化到代数反馈移位寄存器（AFSR）。 FCSR和AFSR的许多基本性质已被确定，并已被用于流密码和准Monte Carlo。 本计画主要研究有关FCSR与AFSR序列的问题，包括：（1）发展新的高度非线性函数类，以应用于分组密码与流密码;（2）发展新的工具，以分析以“带进位”为基础的非线性函数;（3）解决AFSR的“寄存器合成问题”;（4）识别新的一类具有良好随机性的AFSR序列;（5）将密码学中的各种思想和方法推广到向量值函数和序列生成器上。

CIF: Small: Primitives for Cryptography and Communications Principal Investigator: Andrew Klapper, University of Kentucky Pseudorandom sequences and highly nonlinear functions are essential for digital communications and information technology. They are used in stream cipher cryptosystems, spread spectrum systems in cellular telephones, GPS systems, satellite communications, error-correcting codes for digital communication, and 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 or nonlinear functions with particular properties are needed. Yet few general constructions of high quality pseudorandom sequences and highly nonlinear functions are known. This research involves the development and analysis of a large supply of these tools for a variety of applications in cryptography, coding theory, and simulations. In 1994 Klapper and Goresky proposed "feedback-with-carry shift registers"(FCSRs), pseudorandom generators which are easily implemented and which rapidly generate sequences with many desirable properties. These generalizeto algebraic feedback shift registers (AFSRs). Many basic properties of FCSRs and AFSRs have been determined and they have been used in stream ciphersand quasi-Monte Carlo. This project addresses issues concerning FCSR and AFSR sequences including (1) The development of new classes of highly nonlinear functions for use in block ciphers and stream ciphers, (2) the development of new tools for the analysis of nonlinear functions based on the "with-carry" paradigm, (3) the solution of the "register synthesis problem" for AFSRs, (4) the identification of new classes of AFSR sequences with goodrandomness properties, and (5) the extension of various ideas and methods in cryptography to vector valued functions and sequence generators.