A Formula Goes to Court : Partisan Gerrymandering and the Efficiency Gap
A Formula Goes to Court : Partisan Gerrymandering and the Efficiency Gap
复制标题
公式告上法庭:党派选区划分与效率差距
DOI：
10.1029/2006wr004954
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发表时间：
2017
影响因子：
5.4
通讯作者：
Daniel Smith
中科院分区：
文献类型：
--
作者：
Daniel Smith
2017年8月美国国家安全局发布了一个网页，宣布了向量子抵抗算法过渡的初步计划(www.iad.gov/iad/programs/iad-initiatives/cnsa-suite.cfm).2016年12月，美国国家标准与技术研究所(NIST)宣布征集量子抵抗算法的建议书，截止日期为2017年11月30日(www.nist.gov/PQCRYPTO)。开发量子抵抗技术，特别是后量子密码系统的努力，正在成为信息安全的中心研究领域。目前后量子密码学的研究是基于L方法，如代数几何、编码理论和格论中的算法。PQC中使用的数学是多样和复杂的，包括表象理论、调和分析、数学物理、代数论、格子理论和代数几何。即使黎曼假设经常被用来处理复杂的关键问题。在过去的三十年里，公钥密码系统家族，作为20世纪70年代末现代密码学的一个根本性突破，已经成为我们通信网络中日益不可或缺的一部分。互联网以及其他通信系统主要依赖于Diffie-Hellman密钥交换、RSA加密以及使用DSA、ECDSA或相关算法的数字签名。这些密码系统的安全性依赖于某些数论问题的难度，例如整数因式分解或离散对数问题。1994年，Peter Shor证明了量子计算机可以在多项式时间内解决所有这些问题，从而使得基于这些假设的所有密码系统的安全性变得无效。已经出现了一个庞大的国际社会来解决这个问题，希望我们的公钥基础设施可以通过使用新的量子抵抗原语来保持完好。在学术界，这门新科学被称为后量子密码学(PQC)。后量子密码学--数学界面临的新机遇和挑战
August 2017 Notices of the AMs 709 In August 2015 the National Security Agency published a webpage announcing preliminary plans for transitioning to quantum-resistant algorithms (www.iad.gov /iad/programs/iad-initiatives/cnsa-suite.cfm). In December 2016 the National Institute of Standards and Technology (NIST) announced a call for proposals for quantum-resistant algorithms with a deadline of 30 November 2017 (www.nist.gov/pqcrypto). The effort to develop quantum-resistant technologies, and in particular post-quantum cryptosystems, is becoming a central research area in information security. Current research in post-quantum cryptography is based on state-of-thea r t c o m p u t a t i o n a l techniques such as algorithms in algebraic geometry, coding theory, and lattice theory. The mathematics utilized in PQC is diverse and sophisticated, including representation theory, harmonic analysis, mathematical physics, algebraic number theory, lattice theory, and algebraic geometry. Even the Riemann hypothesis is often used to deal with critical problems in complexity Over the past three decades, the family of public-key cryptosystems, a fundamental breakthrough in modern cryptography in the late 1970s, has become an increasingly integral part of our communication networks. The Internet, as well as other communication systems, relies principally on the Diffie-Hellman key exchange, RSA encryption, and digital signatures using DSA, ECDSA, or related algorithms. The security of these cryptosystems depends on the difficulty of certain number-theoretic problems, such as integer factorization or the discrete log problem. In 1994 Peter Shor showed that quantum computers can solve each of these problems in polynomial time, thus rendering the security of all cryptosystems based on such assumptions impotent. A large international community has emerged to address this issue in the hope that our public-key infrastructure may remain intact by utilizing new quantum-resistant primitives. In the academic world, this new science bears the moniker Post-Quantum Cryptography (PQC). Post-Quantum Cryptography—A New Opportunity and Challenge for the Mathematics Community