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  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    [AB09] Sanjeev Arora and Boaz Barak, Computational Complexity: A Modern Approach, Cambridge University Press, 2009.

    [AKS04] Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, Primes is in p, Annals of mathematics (2004), 781–793.

    [Bou04] Nicolas Bourbaki, Theory of sets, Springer, 2004.

    [DH76] Whitfield Diffie and Martin E Hellman, New directions in cryptography, Information Theory, IEEE Transactions on 22 (1976), no. 6, 644–654.

    [FS03] Niels Ferguson and Bruce Schneier, Practical cryptography, vol. 23, Wiley New York, 2003.

    [Gau86] Carl Friedrich Gauß, Disquisitiones Arithmeticae, 1801. English translation by Arthur A. Clarke, 1986.

    [Har05] Godfrey Harold Hardy, A Mathematician’s Apology, 2005, First electronic edition, available at

    [HC] Dan Harkins and Dave Carrel, RFC 2409: The Internet Key Exchange (IKE), November 1998, Status: Proposed Standard.

    [HW79] Godfrey Harold Hardy and Edward Maitland Wright, An introduction to the theory of numbers, Oxford University Press, 1979.

    [LK08] M Lepinski and S Kent, RFC 5114-Additional Diffie-Hellman Groups for Use with IETF Standards, 2008.

    [Lub96] Michael George Luby, Pseudorandomness and Cryptographic Applications, Princeton University Press, 1996.

    [MVOV96] Alfred J Menezes, Paul C Van Oorschot, and Scott A Vanstone, Handbook of applied cryptography, CRC press, 1996.

    [NC10] Michael A Nielsen and Isaac L Chuang, Quantum computation and quantum information, Cambridge university press, 2010.

    [PS04] Jonathan A Poritz and Morton Swimmer, Hash woes, Virus Bulletin (2004), 14–16.

    [RSA78] Ronald L Rivest, Adi Shamir, and Len Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM 21 (1978), no. 2, 120–126.

    [Sha48] C. E. Shannon, A mathematical theory of communication, Bell Systems Technical Journal 27 (1948), 379–423, 623–656.

    [Sha49]_____, Communication theory of secrecy systems, Bell System Technical Journal 28 (1949), no. 4, 656–715.

    [Sho94] Peter W Shor, Algorithms for quantum computation: discrete logarithms and factoring, Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on, IEEE, 1994, pp. 124–134.

    [Sho09] Victor Shoup, A computational introduction to number theory and algebra, Cambridge University Press, 2009, on-line at

    [Sta02] Richard Stallman, Free Software, Free Society: Selected Essays of Richard M. Stallman, Lulu. com, 2002.

    [WY05] Xiaoyun Wang and Hongbo Yu, How to break md5 and other hash functions, Advances in Cryptology–EUROCRYPT 2005, Springer, 2005, pp. 19–35.

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