Advanced cryptography - Project

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1 Advanced cryptography - Project Vanessa Vitse Master SCCI Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 1 / 12

2 Assignment Survey of some research topics related to elliptic and hyperelliptic curve cryptography. Work to do read 1-2 papers on the given topic write a report (<5 pages) describing the general problem and contributions of the papers implement the main algorithm and illustrate it on at least one example give a 20 min presentation (with illustration of your implementation) and answer to 5-10 min questions listen to other talks and ask at least one question during the 6h of presentation Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 2 / 12

3 1 Index calculus methods for attacking DLP on elliptic curves defined over extension fields E(F q n) 2 people P. Gaudry. Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem. J. Symbolic Comput., 44(12): , K. Nagao. Decomposition attack for the Jacobian of a hyperelliptic curve over an extension field. In Algorithmic Number Theory ANTS-IX, vol of Lecture Notes in Comput. Sci., , Springer, Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 3 / 12

4 2 Non-hyperelliptic curves 2 people 1st part: Arithmetic on the Jacobian variety S. Arita. An addition algorithm in Jacobian of C ab curves. Discrete Appl. Math., 130(1):13 31, R. Cohen. Group law algorithms for Jacobian varieties of curves over finite fields. In Algebraic Geometry and its Applications, vol. 5 of Ser. Number Theory Appl., , World Sci. Pub., Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 4 / 12

5 2 Non-hyperelliptic curves 2 people 2nd part: Index calculus methods for attacking DLP on these groups C. Diem. An index calculus algorithm for plane curves of small degree. In Algorithmic Number Theory ANTS VII, vol of Lecture Notes in Comput. Sci., , Springer, Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 5 / 12

6 3 Isogeny volcanoes 2 people A. Sutherland. Isogeny volcanoes. In Algorithmic Number Theory ANTS X, vol. 1 of Open Book Ser., , Math. Sci. Pub., Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 6 / 12

7 4 Construction of pairing-friendly curves 2 people A. Miyaji, M. Nakabayashi, S. Takano. New explicit conditions of elliptic curve traces for FR-reduction. IEICE Transactions on Fundamentals, E84-A(5), , P. Barreto, M. Naehrig. Pairing-friendly elliptic curves of prime order. In Selected Areas in Cryptography SAC 2005, vol of Lecture Notes in Comput. Sci., , Springer, Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 7 / 12

8 5 Different coordinates for faster elliptic curve operations 1 person C. Doche, T. Lange. Arithmetic of Elliptic Curves. Chapter 13 of Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman & Hall/CRC, D. Bernstein, P. Birkner, M. Joye, T. Lange, C. Peters. Twisted Edwards curves. In Progress in Cryptology AFRICACRYPT 2008, vol of Lecture Notes in Comput. Sci., , Springer, Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 8 / 12

9 6 Faster hyperelliptic curve arithmetic 1 person S. Duquesne, T. Lange. Arithmetic of Hyperelliptic Curves. Chapter 14 of Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman & Hall/CRC, M. Jacobson, A. van den Poorten. Computational aspects of NUCOMP. In Algorithmic Number Theory ANTS V, vol of Lecture Notes in Comput. Sci., , Springer, Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 9 / 12

10 7 Hashing to elliptic curves 1 person T. Icart. How to hash into elliptic curves. In Advances in Cryptology CRYPTO 2009, vol of Lecture Notes in Comput. Sci., , Springer, E. Brier, J.-S. Coron, T. Icart, D. Madore, H. Randriam, M. Tibouchi. Efficient indifferentiable hashing into ordinary elliptic curves. In Advances in Cryptology CRYPTO 2010, vol of Lecture Notes in Comput. Sci., , Springer, Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 10 / 12

11 8 Side-channel attacks and counter-measures 2 people H. Cohen, G. Frey et al. Chapters 28 and 29 of Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman & Hall/CRC, I. Blake, G. Seroussi, N. Smart. Chapters 4 and 5 of Advances in Elliptic Curve Cryptography, Cambridge University Press, Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 11 / 12

12 9 Faster pairings 1 person M. Scott. Implementing cryptographic pairings. In Pairing-based cryptography Pairing 2007, vol of Lecture Notes in Comput. Sci., , Springer, F. Vercauteren. Optimal pairings. IEEE Trans. Inform. Theory 56(1): , Vanessa VITSE (Institut Fourier) Advanced cryptography Master SCCI 12 / 12