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## ECM3726 - Cryptography (2018)

MODULE TITLE | Cryptography | CREDIT VALUE | 15 |
---|---|---|---|

MODULE CODE | ECM3726 | MODULE CONVENER | Dr Gihan Marasingha (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS | 0 | 11 | 0 |

Number of Students Taking Module (anticipated) | 120 |
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Cryptography is fundamental to life in the information age. The communications we send and receive daily via the Internet and mobile networks are secured using cryptographic algorithms. Cryptanalysis is the study of tools aimed at deciphering or ‘cracking’ secret messages and cryptosystems. Public-key algorithms have other uses, including authentication and key-exchange.

Underlying these tools is a firm foundation in number theory and the theory of elliptic curves. You will have the opportunity to write cryptographic code in the Python programming language.

Prerequisite modules: ECM3704 Number Theory and ECM2712 Linear Algebra.

This module aims to develop the theory and practice of public-key and symmetric-key cryptography. The tools encountered will be valuable for employment in the security sector or for further study in cryptography or number theory.

On successful completion of this module, **you should be able to**:

**Module Specific Skills and Knowledge:**

1 state all definitions pertaining to cryptography;

2 describe cryptographic algorithms and apply them to given problems;

3 implement cryptographic algorithms using a computer programming language;

4 prove relevant theorems and prove the correctness of cryptographic algorithms.

5 describe algorithms to solve unseen problems;

**Discipline Specific Skills and Knowledge**:

4 understand the application of pure mathematics to practical problems;

5 analyse algorithms;

**Personal and Key Transferable / Employment Skills and Knowledge**:

6 demonstrate computer programming skills;

7 formulate precise descriptions of complex problems and thereby solve them;

8 use a range of learning resources;

9 manage time effectively.

- the complexity of algorithms;

- mono- and polyalphabetic substitution ciphers;

- the Vigenère cipher;

- block cipher modes of operation;

- affine block ciphers;

- the Hill cipher;

- computing with finite fields and the AES cipher;

- classes of cryptanalytic attacks

- Diffie-Hellman key exchange

- the ElGamal public-key cryptosystem;

- cryptanalysis of DLP-based problems:

- Shanks baby-step, giant-step algorithm;

- Pohlig-Hellman

- the RSA cryptosystem;

- trial division, Fermat factorisation;

- Pollard’s p-1 method;

- Pollard’s rho method;

- primality testing (Fermat, Miller-Rabin)

- authentication:

- man-in-the-middle attacks

- digital signatures (ElGamal and RSA);

- forgeries;

- the arithmetic of elliptic curves;

- the elliptic curve method for factorisation;

- elliptic curve cryptography.

Scheduled Learning & Teaching Activities | 33.00 | Guided Independent Study | 117.00 | Placement / Study Abroad | 0.00 |
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Category | Hours of study time | Description |

Scheduled learning and teaching activities | 33 | Lectures including example classes |

Guided independent study | 117 | Reading, working on example sheets, computer programming. |

Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|

Exercise sheets | 5 x 10 hours | All | Model answers provided on ELE. |

Coursework | 20 | Written Exams | 80 | Practical Exams |
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Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Written exam – closed book | 80 | 2 hours | All | Via SRS |

Coursework – example sheets | 20 | All | Written | |

Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-reassessment |
---|---|---|---|

All above | Written exam (100%) | All | August Ref/Def period |

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

information that you are expected to consult. Further guidance will be provided by the Module Convener

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Hoffstein, J., Pipher, J. & Silverman, J.H. | An introduction to mathematical cryptography | 2nd | Springer | 2014 | 978-1493917105 | [Library] |

Set | Buchmann, J | Introduction to Cryptography | 2nd | Springer | 2004 | 978-0387207568 | [Library] |

Set | Koblitz, N. | A course in number theory and cryptography | 2nd | Springer | 1994 | 978-0387942933 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
---|---|---|---|

PRE-REQUISITE MODULES | ECM2712, ECM3704 |
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CO-REQUISITE MODULES |

NQF LEVEL (FHEQ) | 6 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Thursday 06 July 2017 | LAST REVISION DATE | Wednesday 27 February 2019 |

KEY WORDS SEARCH | Cryptosystems (symmetric and public-key), encryption, decryption, RSA, discrete logarithm problems, elliptic curve cryptography, factorisation methods, Miller-Rabin test, digital signature schemes |
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