| Reference : Hachage vers les courbes elliptiques et cryptanalyse de schémas RSA |
| Dissertations and theses : Doctoral thesis | |||
| Engineering, computing & technology : Computer science | |||
| http://hdl.handle.net/10993/15584 | |||
| Hachage vers les courbes elliptiques et cryptanalyse de schémas RSA | |
| English | |
| Tibouchi, Mehdi [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)] | |
| 23-Sep-2011 | |
| University of Luxembourg, Luxembourg, Luxembourg | |
| Université Paris 7-Denis Diderot, France | |
| Docteur en Informatique | |
Coron, Jean-Sébastien  | |
| Naccache, David | |
| [en] Cryptography ; Elliptic Curves ; Random Oracle ; Provable Security ; Cryptanalysis ; RSA ; Cryptosystem ; EMV Specifications ; Physical Attacks | |
| [en] This thesis consists of two independent parts, devoted to both aspects of cryptology: construction and analysis.
Contributions to cryptography proper, on the one hand, address open questions in algebraic curve-based cryptography, particularly the problem of encoding and hashing to elliptic curves. We derive some quantitative results on curve-valued encoding functions, and give a satisfactory construction of hash functions based on those encodings, using a range of mathematical techniques from function field arithmetic, the algebraic geometry of curves and surfaces, and character sums. We also worked on a more implementation-related problem in elliptic curve cryptography, namely the construction of fast addition and doubling formulas. Our cryptanalytic work, on the other hand, focuses on RSA-based cryptosystems—mostly encryption and signature schemes. We have obtained and carried out new attacks on standardized padding schemes that remain in widespread use, including ISO/IEC 9796-2 for signatures and PKCS#1 v1.5 for encryption. We also propose new physical fault attacks on RSA signature schemes using the Chinese Remainder Theorem, and a stronger attack on RSA schemes relying on small hidden-order subgroups. The tools involved include index calculus, lattice reduction techniques and efficient arithmetic of large degree polynomials. | |
| http://hdl.handle.net/10993/15584 |
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