Lecturer: |
Dr. Alexander D. Rahm
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Lectures: |
24 x 1 hour lectures plus 10 x 1 hour tutorials in Semester 2, plus 70 hours of self study.
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Schedule: |
Lectures Thursdays 1 p.m. in IT202 and Fridays 1 p.m. in AC213. The tutorial takes place in two sessions:
Wednesday 1 p.m.
and Thursday 2 p.m., but only every two weeks. The venue for the tutorial is: ADB-G021, which is the computer lab in the ground floor of the building "Aras de Brun". |
Credit: |
5 ECTS for students in courses 4BME1, 1SD1, 4BMS2, 4BS2 and 3BA1. Module codes CS402, MA492 and MA545.
Links to the administrative sheets of the modules
MA492
,
CS402
and
MA545.
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What you will learn: |
- Encrypt and decrypt simple RSA, Diffie-Hellmann and ElGamal cryptosystems.
- Understand the weaknesses of discrete-logarithm-problem based cryptosystems like RSA and Diffie-Hellmann key exchange.
- Break an ElGamal encryption key by a pre-image attack.
- Define elliptic curves, calculate the group of points of an elliptic curve.
- Explain the use of elliptic curves in public key cryptography.
- Encrypt and decrypt using an elliptic curve cryptosystem.
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Why take this course: |
You will open yourself the door to becoming a well-paid elliptic curve cryptographer.
As discrete-logarithm-problem based cryptosystems like RSA and Diffie-Hellmann key exchange are
under a great risk to break down soon, elliptic curve cryptographers will in the upcoming years be very sought-after by internet service providers, banks, mobile phone companies, secret services and software development firms. |
Assessment: |
Exam (80%) and Continuous Assessment (20%). |
Texts: |
- Douglas R. Stinson, Cryptography: theory and practice, Chapman and Hall. Available at Main Library Open Access (005.82 STI).
- Paul Garrett, Making, Breaking Codes: Introduction to Cryptology, Prentice Hall. Available at Main Library Open Access (652.8 GAR).
- Neal Koblitz, A Course in Number Theory and Cryptography, Springer. Available at Main Library Open Access (512.7 KOB)
- S.C. Coutinho, The Mathematics of Ciphers: Number Theory and RSA Cryptography, A. K. Peters. Available at Main Library Open Access (512.7 COU).
- Tadeusz Struk, Elliptic Curve Cryptography as suitable solution for mobile devices, Unpublished master's thesis, National University of Ireland Galway 2009, James Hardiman Library Online Access.
- Michael Rosing, Implementing elliptic curve cryptography , Greenwich : Manning. Available at Main Library Open Access (005.82 ROS).
- A. J. Menezes, Elliptic curve public key cryptosystems, Boston : Kluwer Academic Publishers. Available at Main Library Open Access (005.82 MEN).
- Accredited Standards Committee on Financial Services, Public key cryptography for the financial services industry : key agreement and key transport using elliptic curve cryptography, Annapolis, MD : Accredited Standards Committee X9, Inc. c2001. Available at Main Library Open Access (005.820218 PUB).
- Henri Cohen, Gerhard Frey, Roberto Avanzi, Handbook of elliptic and hyperelliptic curve cryptography, Boca Raton : Chapman & Hall/CRC 2006.
Available at Main Library Open Access (516.352 HAN).
- Anthony W. Knapp, Elliptic curves, Princeton, N.J. : Princeton University Press 1992.
Available at Main Library Open Access (516.352 KNA) .
- Henry P. McKean, Victor Moll, Elliptic curves: function theory, geometry, arithmetic, Cambridge, U.K ; New York : Cambridge University Press 1997.
Available at Main Library Open Access (516.352 McK).
- Dale Husemoller, Elliptic curves, New York ; London : Springer-Verlag c1987.
Available at Main Library Open Access (512.33 HUS).
- Joseph H. Silverman, John Torrence Tate, Rational points on elliptic curves, New York ; London : Springer-Verlag c1992.
Available at Main Library Open Access (516.352 SIL).
- Joseph H. Silverman, The arithmetic of elliptic curves, New York : Springer-Verlag c1986.
Available at Main Library Open Access (516.35 SIL).
- Gordon Welchman, The hut six story : breaking the enigma codes Cleobury Mortimer : M and M Baldwin 1997.
Available at Main Library Open Access (512.7 WEL).
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Resources: |
Problem sheet on ElGamal systems and RSA for exam preparation.
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ElGamal_cryptosystem_slides.
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Elliptic curves over the real numbers -_slides.
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Elliptic_curves_over_the_rational_numbers_-_slides.
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Elliptic_curves_over_finite_fields_-_slides.
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Elliptic_curve_cryptosystems_-_slides.
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Elliptic_curve_sample_encryption_-_slides.
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Padding_scheme_sample.
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TJ Maxx Data Security Fiasco.
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GAP - Groups, Algorithms, Programming.
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GAP script for the padding scheme in Homework 1.
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Last year's exam questions.
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