Semantic Security and Key-Privacy with Random Split of St-Gen Codes

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9709)


Recently we have defined Staircase-Generator codes (St-Gen codes) and their variant with a random split of the generator matrix of the codes. One unique property of these codes is that they work with arbitrary error sets. In this paper we analyze the semantic security against chosen plaintext attack (IND-CPA) and key-privacy i.e. indistinguishability of public keys under chosen plaintext attack (IK-CPA) of the encryption scheme with random split of St-Gen codes. In a similar manner as it was done by Nojima et al. and later by Yamakawa et al. we show that padding the plaintext with a random bit-string provides IND-CPA and IK-CPA in the standard model. The difference with McEliece scheme is that with our scheme the length of the padded random string is significantly shorter.


Public key cryptography Code based cryptosystems Semantic security Key-privacy 


  1. 1.
    Bellare, M., Boldyreva, A., Desai, A., Pointcheval, D.: Key-privacy in public-key encryption. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, p. 566. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Desai, A., Pointcheval, D., Rogaway, P.: Relations among notions of security for public-key encryption schemes. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, p. 26. Springer, Heidelberg (1998)Google Scholar
  3. 3.
    Gligoroski, D., Samardjiska, S., Jacobsen, H., Bezzateev, S.: McEliece in the world of Escher. Cryptology ePrint Archive: Report 2014/360 (2014).
  4. 4.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Kobara, K., Imai, H.: Semantically secure McEliece public-key cryptosystems -conversions for McEliece PKC. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 19–35. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    McEliece, R.J.: A Public-Key System Based on Algebraic Coding Theory, pp. 114–116. Jet Propulsion Lab (1978). DSN Progress Report 44Google Scholar
  7. 7.
    Moody, D., Perlner, R.: Vulnerabilities of “McEliece in the World of Escher”. Cryptology ePrint Archive: Report 2015/966 (2015).
  8. 8.
    Nojima, R., Imai, H., Kobara, K., Morozov, K.: Semantic security for the McEliece cryptosystem without random oracles. Des. Codes Crypt. 49(1–3), 289–305 (2008)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Samardjiska, S., Gligoroski, D.: Approaching maximum embedding efficiency on small covers using staircase-generator codes. In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 2752–2756, June 2015Google Scholar
  10. 10.
    Samardjiska, S., Gligoroski, D.: An Encryption Scheme Based on Random Split of St-Gen Codes. Cryptology ePrint Archive: Report 2016/202 (2016).
  11. 11.
    Sendrier, N., Tillich, J.-P.: Private communication, October 2014Google Scholar
  12. 12.
    Yamakawa, S., Cui, Y., Kobara, K., Hagiwara, M., Imai, H.: On the Key-Privacy Issue of McEliece Public-Key Encryption. In: Boztaş, S., Lu, H.-F.F. (eds.) AAECC 2007. LNCS, vol. 4851, pp. 168–177. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of TelematicsNTNU, The Norwegian University of Science and TechnologyTrondheimNorway
  2. 2.Faculty of Computer Science and EngineeringUKIMSkopjeMacedonia

Personalised recommendations