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Title of Journal: Des Codes Cryptogr

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Abbravation: Designs, Codes and Cryptography

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Springer US

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DOI

10.1016/j.anihpc.2014.05.002

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1573-7586

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Point compression for the trace zero subgroup over

Authors: Elisa Gorla Maike Massierer
Publish Date: 2014/01/22
Volume: 75, Issue: 2, Pages: 335-357
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Abstract

Using Semaev’s summation polynomials we derive a new equation for the mathbb F qrational points of the trace zero variety of an elliptic curve defined over mathbb F q Using this equation we produce an optimalsize representation for such points Our representation is compatible with scalar multiplication We give a point compression algorithm to compute the representation and a decompression algorithm to recover the original point up to some small ambiguity The algorithms are efficient for trace zero varieties coming from small degree extension fields We give explicit equations and discuss in detail the practically relevant cases of cubic and quintic field extensionsWe thank Pierrick Gaudry and Peter Schwabe for helpful discussions and Tanja Lange for pointing out the work of Naumann We are grateful to the mathematics department of the Univerity of Zürich for access to their computing facilities The authors were supported by the Swiss National Science Foundation under Grant No 123393

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Other Papers In This Journal:
  1. Composition of recursions and nonlinear complexity of periodic binary sequences
  2. Practical-time attacks against reduced variants of MISTY1
  3. On the largest affine sub-families of a family of NFSR sequences
  4. The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
  5. On explicit factors of cyclotomic polynomials over finite fields
  6. Two classes of optimal two-dimensional OOCs
  7. Sequences with small correlation
  8. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  9. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  10. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  11. A new table of permutation codes
  12. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  13. Nonexistence of CW (110, 100)
  14. The Diffie–Hellman problem and generalization of Verheul’s theorem
  15. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  16. Improved lower bounds on sizes of single-error correcting codes
  17. A combinatorial problem related to sparse systems of equations
  18. Some results concerning cryptographically significant mappings over GF(2 n )
  19. A note on the reducibility of binary affine polynomials
  20. Primitive normal bases for quartic and cubic extensions: a geometric approach
  21. Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$
  22. Some cyclic codes of length 2 p n
  23. On the correlation distribution of Delsarte–Goethals sequences
  24. Algebraic decoding of folded Gabidulin codes
  25. Inner balance of symmetric designs
  26. On the construction of Griesmer codes of dimension 5
  27. Applications of representation theory to wireless communications
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