CIF:Small: Primitives for Cryptography and Communications

CIF：小：密码学和通信的原语主要调查者：安德鲁·克拉珀，肯塔基大学的伪随机序列和高度非线性函数对于数字通信和信息技术是必不可少的。它们用于流密码密码系统、蜂窝电话扩频系统、GPS系统、卫星通信、数字通信的纠错码，以及用于天气预报、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的大型模拟。在每种情况下，都需要具有特定性质的序列或非线性函数。然而，高质量伪随机序列和高度非线性函数的一般构造却鲜为人知。这项研究涉及到为密码学、编码理论和模拟中的各种应用提供大量这些工具的开发和分析。1994年，克拉珀和戈雷斯基提出了带进位的反馈移位寄存器(FCSR)，这是一种易于实现的伪随机生成器，可以快速生成具有许多理想特性的序列。这些推广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蒙特卡罗。该项目解决了与FCSR和AFSR序列有关的问题，包括(1)开发用于分组密码和流密码的新型高度非线性函数，(2)开发基于“带进位”范例的用于分析非线性函数的新工具，(3)解决AFSR的“寄存器合成问题”，(4)识别具有良好随机性的新型AFSR序列，以及(5)将密码学中的各种思想和方法扩展到向量值函数和序列生成器。

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.