Acquire a basic knowledge of the concepts and methods related to the theory of public key cryptography using the group of points of an elliptic curve on a finite field. Apply the theory of elliptic curves to classical problems of computational number theory such as factorization and primality testing.
Curriculum
teacher profile teaching materials
- Cubics and elliptic curves
- The group law and equations of elliptic curves
- Isogenies
- Torsion points
- Elliptic curves over finite fields and Hasse's Theorem
- Brief discussion of symmetric and public key cryptosystems
- Algorithms on Elliptic Curves: Double and Add and Schoof Algorithm
- Public Key and Digital Signature algorithms on Elliptic Curves
- Weil Pairing and Identity based elliptic cryptosystems
Programme
- Affine and projective curves- Cubics and elliptic curves
- The group law and equations of elliptic curves
- Isogenies
- Torsion points
- Elliptic curves over finite fields and Hasse's Theorem
- Brief discussion of symmetric and public key cryptosystems
- Algorithms on Elliptic Curves: Double and Add and Schoof Algorithm
- Public Key and Digital Signature algorithms on Elliptic Curves
- Weil Pairing and Identity based elliptic cryptosystems
Core Documentation
Professor notesReference Bibliography
Silverman - The Arithmetic of Elliptic Curves, Springer 1986 Milne - (WSPC; 2nd edition (August 21, 2020) Washington - Elliptic Curves: Number Theory and Cryptography (Chapman and Hall/CRC; 2nd edition 2008)Type of delivery of the course
In person lectures by the professorType of evaluation
Oral exam consisting of a short seminar on a topic chosen together with the professor, and a classical oral exam on the Theorems discussed in class (from a fixed list) teacher profile teaching materials
- Cubics and elliptic curves
- The group law and equations of elliptic curves
- Isogenies
- Torsion points
- Elliptic curves over finite fields and Hasse's Theorem
- Brief discussion of symmetric and public key cryptosystems
- Algorithms on Elliptic Curves: Double and Add and Schoof Algorithm
- Public Key and Digital Signature algorithms on Elliptic Curves
- Weil Pairing and Identity based elliptic cryptosystems
Programme
- Affine and projective curves- Cubics and elliptic curves
- The group law and equations of elliptic curves
- Isogenies
- Torsion points
- Elliptic curves over finite fields and Hasse's Theorem
- Brief discussion of symmetric and public key cryptosystems
- Algorithms on Elliptic Curves: Double and Add and Schoof Algorithm
- Public Key and Digital Signature algorithms on Elliptic Curves
- Weil Pairing and Identity based elliptic cryptosystems
Core Documentation
Professor notesReference Bibliography
Silverman - The Arithmetic of Elliptic Curves, Springer 1986 Milne - (WSPC; 2nd edition (August 21, 2020) Washington - Elliptic Curves: Number Theory and Cryptography (Chapman and Hall/CRC; 2nd edition 2008)Type of delivery of the course
In person lectures by the professorType of evaluation
Oral exam consisting of a short seminar on a topic chosen together with the professor, and a classical oral exam on the Theorems discussed in class (from a fixed list) teacher profile teaching materials
- Cubics and elliptic curves
- The group law and equations of elliptic curves
- Isogenies
- Torsion points
- Elliptic curves over finite fields and Hasse's Theorem
- Brief discussion of symmetric and public key cryptosystems
- Algorithms on Elliptic Curves: Double and Add and Schoof Algorithm
- Public Key and Digital Signature algorithms on Elliptic Curves
- Weil Pairing and Identity based elliptic cryptosystems
Programme
- Affine and projective curves- Cubics and elliptic curves
- The group law and equations of elliptic curves
- Isogenies
- Torsion points
- Elliptic curves over finite fields and Hasse's Theorem
- Brief discussion of symmetric and public key cryptosystems
- Algorithms on Elliptic Curves: Double and Add and Schoof Algorithm
- Public Key and Digital Signature algorithms on Elliptic Curves
- Weil Pairing and Identity based elliptic cryptosystems
Core Documentation
Professor notesReference Bibliography
Silverman - The Arithmetic of Elliptic Curves, Springer 1986 Milne - (WSPC; 2nd edition (August 21, 2020) Washington - Elliptic Curves: Number Theory and Cryptography (Chapman and Hall/CRC; 2nd edition 2008)Type of delivery of the course
In person lectures by the professorType of evaluation
Oral exam consisting of a short seminar on a topic chosen together with the professor, and a classical oral exam on the Theorems discussed in class (from a fixed list)