FACULTY of SCIENCE Syllabus

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FACULTY OF SCIENCE Department of Mathematics and Statistics Pure Mathematics 649 Advanced Cryptography and Cryptoanalysis (see Course Descriptions under the year applicable: http://www.ucalgary.ca/pubs/calendar/ ) Syllabus Topics Number of Hours Residuacity Based Cryptography: Miller-Rabin signature scheme, Rabin-Williams 6 cryptosystem. The quadratic residuacity problem, Blum-Blum-Shub pseudorandom number generator, Goldwasser-Micali cryptosystem. Factoring and Discrete Log Algorithms: Number Field Sieve, Function Field Sieve, 9 Adleman-DesMarrais algorithm and their respective complexities. Hyperelliptic Curve Cryptography: Introduction to hyperelliptic curves. Divisors and 9 the Mumford representation. Divisor addition, reduction and Cantor’s algorithm. Hyperelliptic curve based cryptographic protocols. The Hyperelliptic Curve Discrete Logarithm Problem. If time permits: the real model of a hyperelliptic curve; principal infrastructure, infrastructure discrete logarithm problem. Pairing Based Cryptography: Divisors revisited. The Weil and Tate pairings. Miller’s 5 algorithm. MOV and Frey-Ruck attacks. ID based cryptography using pairings. Tripartite key exchange via pairings. Student Presentations: 6 TOTAL: 35 Additional Topics (if time permits): Provable Security: Formal notions of security against active and passive attacks, formal proofs of security. Secret Sharing: Definition of a secret sharing scheme. Perfect secret sharing schemes. Shamir’s scheme. Niederreiter’s scheme. Access structures. Code-Based Cryptography: Basic coding theory. McEliece cryptosystem. Goppa codes. Lattice-Based Cryptography: Overview of lattices, shortest vector and closest vector problems. Reduction (LLL-algorithm). Ajtai-Dwork construction. NTRU. Possibly other lattice based schemes. Multi-variate Cryptography: Hidden Field Equations. Matsumoto-Imai scheme. Possibly other MV based system. Groebner bases. Attacks on multi-variate polynomial based schemes. * * * * * * * * * * 2010:08:12 Effective: Fall 2010 RS:jml Name change/description change/combined with PMAT 529: 2011:07:01 WEC .

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Etsi Gr Qsc 001 V1.1.1 (2016-07)
ETSI GR QSC 001 V1.1.1 (2016-07) GROUP REPORT Quantum-Safe Cryptography (QSC); Quantum-safe algorithmic framework 2 ETSI GR QSC 001 V1.1.1 (2016-07) Reference DGR/QSC-001 Keywords algorithm, authentication, confidentiality, security ETSI 650 Route des Lucioles F-06921 Sophia Antipolis Cedex - FRANCE Tel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16 Siret N° 348 623 562 00017 - NAF 742 C Association à but non lucratif enregistrée à la Sous-Préfecture de Grasse (06) N° 7803/88 Important notice The present document can be downloaded from: http://www.etsi.org/standards-search The present document may be made available in electronic versions and/or in print. The content of any electronic and/or print versions of the present document shall not be modified without the prior written authorization of ETSI. In case of any existing or perceived difference in contents between such versions and/or in print, the only prevailing document is the print of the Portable Document Format (PDF) version kept on a specific network drive within ETSI Secretariat. Users of the present document should be aware that the document may be subject to revision or change of status. Information on the current status of this and other ETSI documents is available at https://portal.etsi.org/TB/ETSIDeliverableStatus.aspx If you find errors in the present document, please send your comment to one of the following services: https://portal.etsi.org/People/CommiteeSupportStaff.aspx Copyright Notification No part may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm except as authorized by written permission of ETSI.
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