A New Public-Key Cryptosystem Based on the Problem of Reconstructing p–Polynomials

1. Augot, D., Finiasz, M.: A public key encryption scheme bases on the polynomial reconstruction problem. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 222–233. Springer, Heidelberg (2003)

   Google Scholar 

2. Augot, D., Finiasz, M., Loidreau, P.: Using the trace operator to repair the polynomial reconstruction based cryptosystem presented at eurocrypt 2003, Cryptology ePrint Archive, Report 2003/209 (2003), http://eprint.iacr.org/

3. Berger, T., Loidreau, P.: Designing an efficient and secure public-key cryptosystem based on reducible rank codes. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 218–229. Springer, Heidelberg (2004)

   Chapter  Google Scholar 

4. Coron, J.-S.: Cryptanalysis of a public-key encryption scheme based on the polynomial reconstruction problem. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 14–28. Springer, Heidelberg (2004)

   Chapter  Google Scholar 

5. Faure, C.: Etude d’un systéme de chiffrement á clé publique fondé sur le probléme de reconstruction de polynômes linéaires. Master’s thesis, Université Paris 7 (2004)

   Google Scholar 

6. Gabidulin, E.M.: Theory of codes with maximal rank distance. Problems of Information Transmission 21, 1–12 (1985)

   MathSciNet  MATH  Google Scholar 

7. Gabidulin, E.M.: A fast matrix decoding algorithm for rank-error correcting codes. In: Lobstein, A., Litsyn, S.N., Zémor, G., Cohen, G. (eds.) Algebraic Coding 1991. LNCS, vol. 573, pp. 126–133. Springer, Heidelberg (1992)

   Chapter  Google Scholar 

8. Kiayias, A., Yung, M.: Cryptanalyzing the polynomial-reconstruction based public-key system under optimal parameter choice. Cryptology ePrint Archive, Report, 2004/217 (2004), http://eprint.iacr.org/

9. Loidreau, P.: Sur la reconstruction des polynômes linéaires: un nouvel algorithme de décodage des codes de Gabidulin. Comptes Rendus de l’Académie des Sciences: Série I 339(10), 745–750 (2004)

   Article  MathSciNet  MATH  Google Scholar 

10. Øre, Ö.: On a special class of polynomials. Transactions of the American Mathematical Society 35, 559–584 (1933)

    Article  MathSciNet  MATH  Google Scholar 

11. Øre, Ö.: Contribution to the theory of finite fields. Transactions of the American Mathematical Society 36, 243–274 (1934)

    Article  MathSciNet  MATH  Google Scholar 

12. Ourivski, A., Johannson, T.: New technique for decoding codes in the rank metric and its cryptography applications. Problems of Information Transmission 38(3), 237–246 (2002)

    Article  MathSciNet  MATH  Google Scholar 

13. Richter, G., Plass, S.: Error and erasure decoding of rank-codes with a modified Berlekamp-Massey algorithm. In: 5th Int. ITG Conference on Source and Channel Coding (SCC 2004) (2004)

    Google Scholar 

14. Roth, R.M.: Maximum-Rank array codes and their application to crisscross error correction. IEEE Transactions on Information Theory 37(2), 328–336 (1991)

    Article  MathSciNet  MATH  Google Scholar 

Download references