Factoring pq² with Quadratic Forms: Nice Cryptanalyses
JOUX, Antoine
Parallélisme, Réseaux, Systèmes, Modélisation [PRISM]
Délégation générale de l'armement [DGA]
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Parallélisme, Réseaux, Systèmes, Modélisation [PRISM]
Délégation générale de l'armement [DGA]
JOUX, Antoine
Parallélisme, Réseaux, Systèmes, Modélisation [PRISM]
Délégation générale de l'armement [DGA]
Parallélisme, Réseaux, Systèmes, Modélisation [PRISM]
Délégation générale de l'armement [DGA]
NGUYEN, Phong Q.
Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities [CASCADE]
< Reduce
Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities [CASCADE]
Language
en
Communication dans un congrès
This item was published in
ASIACRYPT'2009 - 15th Annual International Conference on the Theory and Application of Cryptology and Information Security, A, 2009-12-06, Tokyo. 2009 n° 5912, p. 469-486
English Abstract
We present a new algorithm based on binary quadratic forms to factor integers of the form N = pq². Its heuristic running time is exponential in the general case, but becomes polynomial when special (arithmetic) hints are ...Read more >
We present a new algorithm based on binary quadratic forms to factor integers of the form N = pq². Its heuristic running time is exponential in the general case, but becomes polynomial when special (arithmetic) hints are available, which is exactly the case for the so-called NICE family of public-key cryptosystems based on quadratic fields introduced in the late 90s. Such cryptosystems come in two flavours, depending on whether the quadratic field is imaginary or real. Our factoring algorithm yields a general key-recovery polynomial-time attack on NICE, which works for both versions: Castagnos and Laguillaumie recently obtained a total break of imaginary-NICE, but their attack could not apply to real-NICE. Our algorithm is rather different from classical factoring algorithms: it combines Lagrange's reduction of quadratic forms with a provable variant of Coppersmith's lattice-based root finding algorithm for homogeneous polynomials. It is very efficient given either of the following arithmetic hints: the public key of imaginary-NICE, which provides an alternative to the CL attack; or the knowledge that the regulator of the quadratic field Q(√p) is unusually small, just like in real-NICE.Read less <
English Keywords
Lattices
Public-key Cryptanalysis
Factorisation
Binary Quadratic Forms
Homogeneous Coppersmith's Root Finding
Lattices.
Origin
Hal imported