| First cycle degree courses | Second cycle degree courses | Single cycle degree courses |
| School of Science | ||
| MATHEMATICS | ||
Course unit
CRYPTOGRAPHY
SC04111836, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
CRYPTOGRAPHY
SC04111836, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
Information on the course unit
| Degree course |
Second cycle degree in MATHEMATICS SC1172, Degree course structure A.Y. 2011/12, A.Y. 2018/19 |
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|---|---|---|
| Degree course track | GENERALE [010PD] | |
| Number of ECTS credits allocated | 6.0 | |
| Type of assessment | Mark | |
| Course unit English denomination | CRYPTOGRAPHY | |
| Website of the academic structure | http://matematica.scienze.unipd.it/2018/laurea_magistrale | |
| Department of reference | Department of Mathematics | |
| Mandatory attendance | No | |
| Language of instruction | English | |
| Branch | PADOVA | |
| Single Course unit | The Course unit can be attended under the option Single Course unit attendance | |
| Optional Course unit | The Course unit can be chosen as Optional Course unit |
Lecturers
| Teacher in charge | ALESSANDRO LANGUASCO | MAT/05 |
|---|
Mutuated
| Course unit code | Course unit name | Teacher in charge | Degree course code |
|---|---|---|---|
| SC04111836 | CRYPTOGRAPHY | ALESSANDRO LANGUASCO | SC1172 |
| SC04111836 | CRYPTOGRAPHY | ALESSANDRO LANGUASCO | SC1176 |
| INP7080692 | CRYPTOGRAPHY | ALESSANDRO LANGUASCO | IN2371 |
| INP7080692 | CRYPTOGRAPHY | ALESSANDRO LANGUASCO | IN2371 |
ECTS: details
| Type | Scientific-Disciplinary Sector | Credits allocated | |
|---|---|---|---|
| Educational activities in elective or integrative disciplines | INF/01 | Computer Science | 1.0 |
| Educational activities in elective or integrative disciplines | MAT/02 | Algebra | 2.0 |
| Educational activities in elective or integrative disciplines | MAT/03 | Geometry | 1.0 |
| Educational activities in elective or integrative disciplines | MAT/05 | Mathematical Analysis | 2.0 |
Course unit organization
| Period | First semester |
|---|---|
| Year | 1st Year |
| Teaching method | frontal |
| Type of hours | Credits | Teaching hours |
Hours of Individual study |
Shifts |
|---|---|---|---|---|
| Practice | 1.0 | 8 | 17.0 | No turn |
| Lecture | 5.0 | 40 | 85.0 | No turn |
| Start of activities | 01/10/2018 |
|---|---|
| End of activities | 18/01/2019 |
| Show course schedule | 2019/20 Reg.2011 course timetable |
Examination board
| Board | From | To | Members of the board |
|---|---|---|---|
| 5 Crittografia - a.a. 2018/2019 | 01/10/2018 | 30/09/2019 |
LANGUASCO
ALESSANDRO
(Presidente)
TONOLO ALBERTO (Membro Effettivo) FILE' GILBERTO (Supplente) PUTTI MARIO (Supplente) RANZATO FRANCESCO (Supplente) |
| Prerequisites: | The topics of the following courses: Algebra (congruences, groups and cyclic groups, finite fields), Calculus (differential and integral calculus, numerical series) both for the BA in Mathematics. |
| Target skills and knowledge: | The main goal of the Cryptography course is to give an overview
of the theoretical basis of the field in order to allow a critical study of the cryptographic protocols used in many applications (authentication, digital commerce). In the first part we will give the mathematical basic tools (essentially from elementary and analytic number theory) that are required to understand modern public-key methods. In the second part we will see how to apply this know-how to study and criticize some protocols currently used. |
| Examination methods: | Written exam |
| Assessment criteria: | During the written exam the student will have to reply to some questions about the topics taught during the lectures.
The maximal mark (30/30) will be conferred to error-free exams only. If the written exam will not be sufficient to decide the evaluation mark, the teacher will ask to the candidate some further questions to be directly replied on the blackboard. |
| Course unit contents: | First Part: Basic theoretical facts: Modular arithmetic. Prime numbers. Little Fermat theorem. Chinese remainder theorem. Finite fields: order of an element and primitive roots. Pseudoprimality tests. Agrawal-Kayal-Saxena's test. RSA method: first description, attacks. Rabin's method and its connection with the integer factorization. Discrete logarithm methods. How to compute the discrete log in a finite field. Elementary factorization methods. Some remarks on Pomerance's quadratic sieve.
Second Part: Protocols and algorithms. Fundamental crypto algorithms. Symmetric methods (historical ones, DES, AES) . Asymmetric methods. Attacks. Digital signature. Pseudorandom generators (remarks). Key exchange, Key exchange in three steps, secret splitting, secret sharing, secret broadcasting, timestamping. Signatures with RSA and discrete log. |
| Planned learning activities and teaching methods: | Classroom lectures. |
| Additional notes about suggested reading: | We will use the following textbooks:
1) A.Languasco, A.Zaccagnini - Manuale di Crittografia - Hoepli Editore, 2015. (italian). 2) N.Koblitz - A Course in Number Theory and Cryptography, Springer, 1994. 3) R.Crandall, C.Pomerance - Prime numbers: A computational perspective - Springer, 2005. 4) B. Schneier - Applied Cryptography - Wiley, 1994 |
| Textbooks (and optional supplementary readings) |
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