Modern Cryptography

W. Patterson, Cynthia E. Winston-Proctor
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Abstract

We live in an age where we willingly provide our social security number, credit card information, home address and countless other sensitive information over the Internet. Whether you are buying a phone case from Amazon, sending in an on-line job application, or logging into your on-line bank account, you trust that the sensitive data you enter is secure. As our technology and computing power become more sophisticated, so do the tools used by potential hackers to our information. In this paper, the underlying mathematics within ciphers will be looked at to understand the security of modern ciphers. An extremely important algorithm in today’s practice is the Advanced Encryption Standard (AES), which is used by our very own National Security Agency (NSA) for data up to TOP SECRET. Another frequently used cipher is the RSA cryptosystem. Its security is based on the concept of prime factorization, and the fact that it is a hard problem to prime factorize huge numbers, numbers on the scale of 22048 or larger. Cryptanalysis, the study of breaking ciphers, will also be studied in this paper. Understanding effective attacks leads to understanding the construction of these very secure ciphers.
现代密码学
我们生活在一个愿意在互联网上提供我们的社会保险号、信用卡信息、家庭住址和无数其他敏感信息的时代。无论你是从亚马逊购买手机壳,发送在线求职申请,还是登录在线银行账户,你都相信你输入的敏感数据是安全的。随着我们的技术和计算能力变得越来越复杂,潜在黑客用来获取我们信息的工具也越来越复杂。在本文中,将研究密码中的基础数学,以了解现代密码的安全性。在今天的实践中,一个极其重要的算法是高级加密标准(AES),它被我们自己的国家安全局(NSA)用于最高机密的数据。另一个常用的密码是RSA密码系统。它的安全性是基于质因数分解的概念,事实上,对22048或更大的数字进行质因数分解是一个困难的问题。本文还将研究密码分析,即破解密码的研究。了解有效的攻击有助于理解这些非常安全的密码的构造。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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