Introduction

For a twenty-minute introduction, read the following paper: Daniel J. Bernstein. "Introduction to post-quantum cryptography." http://www.springer.com/math/numbers/book/978-3-540-88701-0?detailsPage=samplePages [PDF mirror] This paper is the introductory chapter of the following book: Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen (editors). Post-quantum cryptography. Springer, Berlin, 2009. ISBN 978-3-540-88701-0.

For much more information, read the rest of the book! There are five detailed chapters surveying the state of the art in quantum computing, hash-based cryptography, code-based cryptography, lattice-based cryptography, and multivariate-quadratic-equations cryptography. The book has a 2009 publication date but was already available in November 2008 from booksellers such as Amazon.

For earlier analyses of the impact of quantum computers on cryptography, see the following papers:

Hong Zhu. "Survey of computational assumptions used in cryptography broken or not by Shor's algorithm." Master's thesis. 2001. http://crypto.cs.mcgill.ca/~crepeau/PDF/memoire-hong.pdf.

Marco A. Barreno. "The future of cryptography under quantum computers." Senior thesis. 2002. http://www.cs.dartmouth.edu/~sws/theses/marco.pdf.

Michael S. Brown. "Classical cryptosystems in a quantum setting." Master's thesis. 2004. http://arxiv.org/pdf/quant-ph/0404061.

Johannes Buchmann, Carlos Coronado, Martin Doering, Daniela Engelbert, Christoph Ludwig, Raphael Overbeck, Arthur Schmidt, Ulrich Vollmer, Ralf-Philipp Weinmann. "Post-quantum signatures." 2004. http://itslab.csce.kyushu-u.ac.jp/iwap04/PostQuantumSignatures.pdf.

Survey talks

PQCrypto 2008: Daniel J. Bernstein's invited talk "A brief survey of post-quantum cryptography" (PDF slides).

INDOCRYPT 2008: Tanja Lange's invited talk "Post-quantum cryptography" (PDF slides).

Challenges for cryptanalysts

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