References of "Tibouchi, Mehdi 2000E839"
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See detailBatch Fully Homomorphic Encryption over the Integers
Cheon, Jung Hee; Coron, Jean-Sébastien UL; Kim, Jinsu et al

in EUROCRYPT (2013)

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See detailA Note on the Bivariate Coppersmith Theorem
Coron, Jean-Sébastien UL; Kirichenko, Alexey; Tibouchi, Mehdi UL

in Journal of Cryptology (2013), 26(2), 246-250

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See detailHachage vers les courbes elliptiques et cryptanalyse de schémas RSA
Tibouchi, Mehdi UL

Doctoral thesis (2011)

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 ... [more ▼]

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. [less ▲]

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See detailFully Homomorphic Encryption over the Integers with Shorter Public Keys
Coron, Jean-Sébastien UL; Mandal, Avradip UL; Naccache, David et al

in CRYPTO (2011)

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See detailEfficient Indifferentiable Hashing into Ordinary Elliptic Curves
Brier, Eric; Coron, Jean-Sébastien UL; Icart, Thomas UL et al

in CRYPTO (2010)

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See detailPractical Cryptanalysis of ISO/IEC 9796-2 and EMV Signatures
Coron, Jean-Sébastien UL; Naccache, David; Tibouchi, Mehdi UL et al

in Proceedings of CRYPTO 2009 (2009)

In 1999, Coron, Naccache and Stern discovered an existential signature forgery for two popular RSA signature standards, ISO/IEC 9796-1 and 2. Following this attack ISO/IEC 9796-1 was withdrawn. ISO/IEC ... [more ▼]

In 1999, Coron, Naccache and Stern discovered an existential signature forgery for two popular RSA signature standards, ISO/IEC 9796-1 and 2. Following this attack ISO/IEC 9796-1 was withdrawn. ISO/IEC 9796-2 was amended by increasing the message digest to at least 160 bits. Attacking this amended version required at least 2^{61} operations. In this paper, we exhibit algorithmic refinements allowing to attack the amended (currently valid) version of ISO/IEC 9796-2 for all modulus sizes. A practical forgery was computed in only two days using 19 servers on the Amazon EC2 grid for a total cost of $\simeq$ US$800. The forgery was implemented for e?= 2 but attacking odd exponents will not take longer. The forgery was computed for the RSA-2048 challenge modulus, whose factorization is still unknown. The new attack blends several theoretical tools. These do not change the asymptotic complexity of Coron et al.’s technique but significantly accelerate it for parameter values previously considered beyond reach. While less efficient (US$45,000), the acceleration also extends to EMV signatures. EMV is an ISO/IEC 9796-2-compliant format with extra redundancy. Luckily, this attack does not threaten any of the 730 million EMV payment cards in circulation for operational reasons. Costs are per modulus: after a first forgery for a given modulus, obtaining more forgeries is virtually immediate. [less ▲]

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