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An algorithm for computing a sequence of Richelot isogenies
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We show that computation of a sequence of Richelot isogenies from specified supersingular Jacobians of genus-2 curves over F_(p) can be executed in F_{p^2} or F_{p^4}. Based on this, we describe a practical algorithm for computing a Richelot isogeny sequence.
Abstract
We show that computation of a sequence of Richelot isogenies from specified supersingular Jacobians of genus-2 curves over F_(p) can be executed in F_{p^2} or F_{p^4}. Based on this, we describe a practical algorithm for computing a Richelot isogeny sequence.
참고문헌 (16)
- P. R. Bending, "Curves of genus 2 with p2 multiplication", 박사, pp.1998
- J.-B. Bost, "Moyenne arithm´etico-g´eom´etrique et p´eriodes des courbes de genre 1 et 2", Gaz. Math., (38), pp.36~64 (1988)
- J. W. S. Cassels, "Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2", London Mathematical Society Lecture Note Series, 230 (1996), Cambridge University Press
- H. Cohen, "Handbook of Elliptic and Hyperelliptic Curve Cryptography" (2006), Chapman & Hall
- D. X. Charles, "Cryptographic hash functions from expander graphs", Journal of Cryptology
- D. X. Charles, "Families of Ramanujan graphs and quaternion algebras", AMSCRM volume “Groups and Symmetries” in honor of John McKay, ~
- Y. J. Choie, "Supersingular hyperelliptic curves of genus 2 over finite fields", Appl. Math. Comput, 163(2), pp.565~576 (2005)
- T. Ibukiyama, "Supersingular curves of genus two and class numbers", Compositio Math, 57(2), pp.127~152 (1986)
- S. Paulus, "Real and imaginary quadratic representations of hyperelliptic function fields", Math. Comp, 68(227), pp.1233~1241 (1999)
- S. Paulus, "Comparing real and imaginary arithmetics for divisor class groups of hyperelliptic curves, Algorithmic number theory", Lecture Notes in Comput. Sci, 1423, pp.576~591 (1998), Springer
- A. Rostovtsev, "Public-key cryptosystem based on isogenies", IACR ePrint, 145~ (2006)
- B. Smith, "Explicit endomorphisms and correspondences", 박사, pp.2005
- J. Tate, "Endomorphisms of abelian varieties over finite fields", Invent. Math, 2, pp.134~144 (1966)
- J. V´elu, "Isog´enies entre courbes elliptiques", C. R. Acad. Sci. Paris S´er. A-B, 273, pp.A238~A241 (1971)
- C. Xing, "On supersingular abelian varieties of dimension two over finite fields", Finite Fields Appl, 2(4), pp.407~421 (1996)
- R. Yoshida, "Simple algorithms for computing a sequence of 2- isogenies", ICISC 2008, 통권 : 5461, pp.52~65 (2009), Springer Verlag
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