Skip to main content
SpringerLink
Log in
Book cover

International Conference on Cryptology and Network Security

CANS 2014: Cryptology and Network Security pp 34–49Cite as

On the Lossiness of 2k-th Power and the Instantiability of Rabin-OAEP

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8813))

Abstract

Seurin (PKC 2014) proposed the 2-Φ/4-hiding assumption which asserts the indistinguishability of Blum Numbers from pseudo Blum Numbers. In this paper, we investigate the lossiness of 2k-th power based on the 2k-Φ/4-hiding assumption, which is an extension of the 2-Φ/4-hiding assumption. And we prove that 2k-th power function is a lossy trapdoor permutation over Quadratic Residuosity group. This new lossy trapdoor function has 2k-bits lossiness for k-bits exponent, while the RSA lossy trapdoor function given by Kiltz et al. (Crypto 2010) has k-bits lossiness for k-bits exponent under Φ-hiding assumption in lossy mode. We modify the square function in Rabin-OAEP by 2k-th power and show the instantiability of this Modified Rabin-OAEP by the technique of Kiltz et al. (Crypto 2010). The Modified Rabin-OAEP is more efficient than the RSA-OAEP scheme for the same secure bits. With the secure parameter being 80 bits and the modulus being 2048 bits, Modified Rabin-OAEP can encrypt roughly 454 bits of message, while RSA-OAEP can roughly encrypt 274 bits.

Supported by the National Basic Research Program of China (973 project)(No.2013CB338002), the National Nature Science Foundation of China (No.61070171, No.61272534).

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. RSA public-key cryptography standards, ftp://ftp.rsasecurity.com/pub/pkcs/pkcs-1

  2. Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  3. Boldyreva, A., Fehr, S., O’Neill, A.: On notions of security for deterministic encryption, and efficient constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 335–359. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  4. Boneh, D.: Simplified OAEP for the RSA and Rabin Functions. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 275–291. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  5. Cachin, C., Micali, S., Stadler, M.: Computationally private information retrieval with polylogarithmic communication. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 402–414. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  6. Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Coppersmith, D.: Small solutions to polynomial equations, and low exponent rsa vulnerabilities. J. Cryptology 10(4), 233–260 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory 22(6), 644–654 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dodis, Y., Reyzin, L., Smith, A.: Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 523–540. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Fischlin, R., Schnorr, C.P.: Stronger security proofs for rsa and rabin bits. J. Cryptology 13(2), 221–244 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Freeman, D.M., Goldreich, O., Kiltz, E., Rosen, A., Segev, G.: More constructions of lossy and correlation-secure trapdoor functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 279–295. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Freeman, D.M., Goldreich, O., Kiltz, E., Rosen, A., Segev, G.: More constructions of lossy and correlation-secure trapdoor functions. J. Cryptology 26(1), 39–74 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Goldreich, O.: The Foundations of Cryptography. Basic Techniques, vol. 1. Cambridge University Press (2001)

    Google Scholar 

  14. Goldreich, O.: The Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press (2004)

    Google Scholar 

  15. Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  16. Herrmann, M.: Improved cryptanalysis of the multi-prime φ - hiding assumption. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 92–99. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Hofheinz, D.: Possibility and impossibility results for selective decommitments. J. Cryptology 24(3), 470–516 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hofheinz, D., Kiltz, E.: The group of signed quadratic residues and applications. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 637–653. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. Joye, M., Libert, B.: Efficient cryptosystems from 2k-th power residue symbols. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 76–92. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  20. Joye, M., Paillier, P.: Fast generation of prime numbers on portable devices: An update. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 160–173. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  21. Kakvi, S.A., Kiltz, E.: Optimal security proofs for full domain hash, revisited. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 537–553. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. Kiltz, E., O’Neill, A., Smith, A.: Instantiability of rsa-oaep under chosen-plaintext attack. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 295–313. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  23. Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coefficients. Mathematische Annalen 261, 515–534 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  24. Lewko, M., O’Neill, A., Smith, A.: Regularity of lossy rsa on subdomains and its applications. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 55–75. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  25. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: STOC, pp. 187–196 (2008)

    Google Scholar 

  26. Seurin, Y.: On the lossiness of the rabin trapdoor function. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 380–398. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  27. Steinfeld, R., Zheng, Y.: On the security of rsa with primes sharing least-significant bits. Appl. Algebra Eng. Commun. Comput. 15(3-4), 179–200 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sun, H.M., Wu, M.E., Steinfeld, R., Guo, J., Wang, H.: Cryptanalysis of short exponent rsa with primes sharing least significant bits. IACR Cryptology ePrint Archive 2008, 296 (2008)

    Google Scholar 

  29. von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 3rd edn. Cambridge University Press (2013)

    Google Scholar 

  30. Xue, H., Li, B., Lu, X., Jia, D., Liu, Y.: Efficient lossy trapdoor functions based on subgroup membership assumptions. In: Abdalla, M., Nita-Rotaru, C., Dahab, R. (eds.) CANS 2013. LNCS, vol. 8257, pp. 235–250. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  31. Yan, S.Y.: Number Theory for Computing, 2nd edn. Springer (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, China

    Haiyang Xue, Bao Li, Xianhui Lu, Kunpeng Wang & Yamin Liu

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Haiyang Xue, Bao Li, Xianhui Lu, Kunpeng Wang & Yamin Liu

  3. University of Chinese Academy of Sciences, Beijing, China

    Haiyang Xue

Authors
  1. Haiyang Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xianhui Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kunpeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yamin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Informatics, Athens University of Economics & Business, 76, Patission Str., 10434, Athens, Greece

    Dimitris Gritzalis

  2. Department of Informatics and Telecommunications, Panepistimiopolis, National and Kapodistrian University of Athens, 15784, Athens, Greece

    Aggelos Kiayias

  3. FORTH-ICS, Vassilika Vouton, P.O. Box 1385, 711 10, Heraklion, Crete, Greece

    Ioannis Askoxylakis

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Xue, H., Li, B., Lu, X., Wang, K., Liu, Y. (2014). On the Lossiness of 2k-th Power and the Instantiability of Rabin-OAEP. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds) Cryptology and Network Security. CANS 2014. Lecture Notes in Computer Science, vol 8813. Springer, Cham. https://doi.org/10.1007/978-3-319-12280-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-12280-9_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12279-3

  • Online ISBN: 978-3-319-12280-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation