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## MTH3026 - Cryptography (2019)

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

MODULE CODE | MTH3026 | MODULE CONVENER | Dr Gihan Marasingha (Coordinator) |

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

DURATION: WEEKS | 0 | 11 weeks | 0 |

Number of Students Taking Module (anticipated) | 116 |
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Cryptography is the science of encryption. In this module, you will learn to formulate encryption as a mathematical problem. Cryptography can be defined as the conversion of data into a scrambled code that can be deciphered and sent across a public or private network.

Cryptography uses two main styles or forms of encrypting data: symmetrical and asymmetrical, and all good encryption schemes use the concept of a key which may take on any one of a number of values. The collection of all possible values is called the keyspace and encryptions and decryptions are represented as functions.

You will focus on two encryption algorithms: so called symmetric and public key algorithms, then you will concentrate on public key algorithms where you cannot deduce one key from another key. Encryption algorithms have huge commercial value; indeed, every day, millions of financial and business transactions are carried out over the internet; and security of internet transactions relies on the highest levels of encryption.

Prerequisite module: MTH3004 Number Theory and MTH2002 Algebra, or equivalent

The aim of this module is to apply elementary number theory to problems in the real world where it is important to transmit information in a secret way. For example, cryptography is used in bank accounts, and is traditionally applied in military science. Note that there is another application of number theory and linear algebra called coding theory - but this is not the same as cryptography.

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

**Module Specific Skills and Knowledge:**

1 formulate encryption as a mathematical problem;

2 demonstrate an understanding of public key cryptography, other practical crypto-systems, some useful impractical ones and some peculiar cryptosystems like the hidden monomial or the combinatorial-algebraic cryptosystem;

3 articulate the complexity of computations in cryptography.

**Discipline Specific Skills and Knowledge:**

4 reveal a grasp of the number-theoretic and algebraic aspects of cryptography.

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

5 show an appreciation of how concrete problems typically require abstract theories for their solution;

6 display a comprehension of how to apply algorithms and why they work.

- introduction to cryptography, history of cryptography Symmetric and anti-symmetric cryptosystems; some simple examples;

- one way functions;

- number theoretic cryptography: introduction to congruences and prime numbers; Euler’s totient function, the integer factorisation and discrete logarithm problems;

- the RSA cryptosystem (Rivest Shamir Adleman), the ElGamal cryptosystem;

- possible attacks and their computational complexity;

- algebraic cryptography: a short review of group and field theory;

- hidden monomial cryptosystem;

- several group-theoretic cryptostems;

- a view of 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/example classes |

Guided independent study | 117 | Lecture and assessment preparation; private study |

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

Coursework – three example sheets | All | Written | |

Coursework | 20 | Written Exams | 80 | Practical Exams | 0 |
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Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Coursework – based on questions submitted for assessment | 20 | 2 assignments, 30 hours total | All | Annotated script and written/verbal feedback |

Written Exam – closed book | 80 | 2 hours | All | Written/verbal on request, SRS |

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

ELE – http://vle.exeter.ac.uk

Reading list for this module:

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

Set | Koblitz, Neal | A course in Number theory and Cryptography | Graduate Text in Mathematics | Springer | 1994 | [Library] | |

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

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

PRE-REQUISITE MODULES | MTH2002, MTH3004 |
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CO-REQUISITE MODULES |

NQF LEVEL (FHEQ) | 6 | AVAILABLE AS DISTANCE LEARNING | No |
---|---|---|---|

ORIGIN DATE | Tuesday 10 July 2018 | LAST REVISION DATE | Friday 30 August 2019 |

KEY WORDS SEARCH | Fermat's little theorem; Miller-Rabin test; cryptosystems (symmetric cryptosystems and public key cryptosystems); encryption; decryption; RSA - and related cryptosystems; discrete logarithmic problems. |
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