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Coursebooks
Caution, these contents corresponds to the coursebooks of last year
Number theory in cryptography
MATH-489
Lecturer(s) :
Serban VladLanguage:
English
Remarque
Cours donné en alternance tous les 2 ans (pas donné en 2018-19)Summary
The goal of the course is to introduce basic notions from public key cryptography (PKC) as well as basic number-theoretic methods and algorithms for cryptanalysis of protocols and schemes based on PKC.Content
Basic notions and algorithms from public key cryptography such as RSA, ElGamal, key exchange protocols, zero knowledge proofs. Main topics may include, but are not limited to
- modular and finite field arithmetic
- primality testing
- polynomial and integer factorization algorithms
- index calculus and discrete logarithm-based schemes
- elliptic curve cryptography
- basic notions from lattice-based cryptography
Keywords
public key cryptography, key exchange, digital signatures, zero knowledge proofs, RSA, ElGamal, integer factorization, index calculus, elliptic curve cryptography
Teaching methods
lecture notes, additional references
Assessment methods
Theoretical assignments: Weekly problem sets focusing on number-theoretic and complexity-theoretic aspects. Theoretical assignments will count for 30% of the final grade.
Programming assignments: All of the programming exercises will be in SAGE which is a Python-based computer algebra system. No prior experience with SAGE or Python is required. Programming assignments will count for 30% of the final grade.
One mid-term exam (15% of the final grade) and one final exam (25% of the final grade). Both exams will test theoretical understanding as well as understanding of the algorithms and protocols. The exams will include no SAGE programming exercises. If needed, algorithms could be presented with pseudo-code.
In the programs
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formWritten
- Credits
5 - Subject examined
Number theory in cryptography - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
Reference week
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21-22 |
legend
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- Lecture in French
- Lecture in English
- Lecture in German