Available on ORBilu since
11 February 2014
Doctoral thesis (Dissertations and theses)
Hachage vers les courbes elliptiques et cryptanalyse de schémas RSA
Tibouchi, Mehdi


Full Text
Author postprint (13.15 MB)

All documents in ORBilu are protected by a user license.

Send to


Keywords :
Cryptography; Elliptic Curves; Random Oracle; Provable Security; Cryptanalysis; RSA; Cryptosystem; EMV Specifications; Physical Attacks
Abstract :
[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.
Disciplines :
Computer science
Author, co-author :
Tibouchi, Mehdi;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Language :
Title :
Hachage vers les courbes elliptiques et cryptanalyse de schémas RSA
Defense date :
23 September 2011
Institution :
Unilu - University of Luxembourg, Luxembourg, Luxembourg
Université Paris 7-Denis Diderot, France
Degree :
Docteur en Informatique
Promotor :


Number of views
122 (4 by Unilu)
Number of downloads
573 (3 by Unilu)


Similar publications

Contact ORBilu