SpringerLink
Log in

Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting

  • Conference paper
Topics in Cryptology – CT-RSA 2012 (CT-RSA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7178))

Included in the following conference series:

Abstract

The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first non-generic fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior in the two party setting. Our second contribution is a complete Paillier [37] threshold encryption scheme in the two-party setting with security against malicious behavior. Our RSA key generation is comprised of the following: (i) a distributed protocol for generation of an RSA composite, and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite as public key and is comprised of: (i) a distributed generation of the corresponding secret-key shares and, (ii) a distributed decryption protocol for decrypting according to Paillier.

The full version of this paper can be found in [31].

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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 ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Algesheimer, J., Camenisch, J., Shoup, V.: Efficient Computation Modulo a Shared Secret with Application to the Generation of Shared Safe-Prime Products. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Baudron, O., Fouque, P.A., Pointcheval, D., Poupard, G., Stern, J.: Practical multi-candidate election system. In: PODC, pp. 274–283. ACM Press (2001)

    Google Scholar 

  3. Blackburn, S., Blake-Wilson, S., Burmester, M., Galbraith, S.: Shared generation of shared RSA keys, http://cacr.math.uwaterloo.ca/techreports/1998/corr98-19.ps

  4. Boneh, D., Franklin, M.K.: Efficient generation of shared RSA keys. J. ACM 48(4), 702–722 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boudot, F.: Efficient Proofs that a Committed Number Lies in an Interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. De Bruijn, N.: On the number of uncanceled elements in the sieve of eratosthenes. Proc. Neder. Akad. Wetensh. 53, 803–812; Reviewed in LeVeque Reviews in Number Theory 4(28), 221

    Google Scholar 

  7. Camenisch, J., Kiayias, A., Yung, M.: On the Portability of Generalized Schnorr Proofs. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 425–442. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Catalano, D., Gennaro, R., Howgrave-Graham, N., Nguyen, P.Q.: Paillier’s cryptosystem revisited. In: ACM Conference on Computer and Communications Security, pp. 206–214 (2001)

    Google Scholar 

  9. Chaum, D., Pedersen, T.P.: Wallet Databases with Observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  10. Cocks, C.: Split Generation of RSA Parameters with Multiple Participants. In: Darnell, M.J. (ed.) IMACC 1997. LNCS, vol. 1355, pp. 200–212. Springer, Heidelberg (1997)

    Google Scholar 

  11. Coppersmith, D.: Small Exponents to Polynomial Equations, and Low Exponent RSA Vulnerabilities. Journal of Cryptology 10, 233–260 (1997)

    Article  MATH  Google Scholar 

  12. Cramer, R., Damgård, I.: On the Amortized Complexity of Zero-Knowledge Protocols. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 177–191. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Cramer, R., Damgård, I.B., Nielsen, J.B.: Multiparty Computation from Threshold Homomorphic Encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280–299. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Cramer, R., Gennaro, R., Schoenmakers, B.: A Secure and Optimally Efficient Multi-Authority Election Scheme. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 103–118. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  15. Damgård, I., Jurik, M.: A Generalisation, a Simplification and some Applications of Paillier’s Probabilistic Public-Key System. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  16. Damgård, I., Jurik, M.: Client/Server Tradeoffs for Online Elections. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 125–140. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Damgård, I., Jurik, M.: A Length-Flexible Threshold Cryptosystem with Applications. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 350–364. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  18. Damgård, I., Mikkelsen, G.L.: Efficient, Robust and Constant-Round Distributed RSA Key Generation. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 183–200. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Damgård, I., Nielsen, J.B.: Perfect Hiding and Perfect Binding Universally Composable Commitment Schemes with Constant Expansion Factor. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 581–596. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  20. Damgård, I., Nielsen, J.B.: Universally Composable Efficient Multiparty Computation from Threshold Homomorphic Encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 247–264. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  21. Desmedt, Y.G.: Threshold cryptography. European Transactions on Telecommunications 5(4), 449–457 (1994)

    Article  Google Scholar 

  22. El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Trans. Info. Theory IT 31, 469–472 (1985)

    MathSciNet  Google Scholar 

  23. Feige, U., Fiat, A., Shamir, A.: Zero-knowledge proofs of identity. J. Cryptology 1(2), 77–94 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  24. Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)

    Chapter  Google Scholar 

  25. Fouque, P.A., Poupard, G., Stern, J.: Sharing Decryption in the Context of Voting or Lotteries. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 90–104. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  26. Frankel, Y., Mackenzie, P.D., Yung, M.: Robust efficient distributed RSA-key generation. In: STOC 1998, pp. 663–672. ACM Press (1998)

    Google Scholar 

  27. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Robust Threshold DSS Signatures. Information and Computation 164(1), 54–84 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure Distributed Key Generation for Discrete-Log Based Cryptosystems. Journal of Cryptology 20(1), 51–83 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. Gennaro, R., Krawczyk, H., Rabin, T.: Robust and Efficient Sharing of RSA Functions. Journal of Cryptology 13(2), 273–300 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  30. Gilboa, N.: Two Party RSA Key Generation. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 116–129. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  31. Hazay, C., Mikkelsen, G.L., Rabin, T., Toft, T.: Efficient RSA key generation and threshold Paillier in the two-party setting. Cryptology ePrint Archive, Report 2011/494 (2011)

    Google Scholar 

  32. Hazay, C., Toft, T.: Computationally Secure Pattern Matching in the Presence of Malicious Adversaries. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 195–212. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  33. Jarecki, S., Liu, X.: Efficient Oblivious Pseudorandom Function with Applications to Adaptive OT and Secure Computation of Set Intersection. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 577–594. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  34. Jarecki, S., Shmatikov, V.: Efficient Two-Party Secure Computation on Committed Inputs. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 97–114. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  35. Lipmaa, H.: On Diophantine Complexity and Statistical Zero-Knowledge Arguments. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 398–415. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  36. Nicolosi, A.A.: Efficient RSA Key Generation Protocol in a Two-Party Setting and its Application into the Secure Multiparty Computation Environment – Master Thesis. Department of Computer Science Aarhus University, Denmark (2011)

    Google Scholar 

  37. Paillier, P.: Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 223. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  38. Poupard, G., Stern, J.: Generation of Shared RSA Keys by Two Parties. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 11–24. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  39. Rabin, T.: A Simplified Approach to Threshold and Proactive RSA. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 89–104. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  40. Schnorr, C.P.: Efficient signature generation by smart cards. Journal of Cryptology 4, 161–174 (1991)

    Article  MATH  Google Scholar 

  41. Shoup, V.: Practical Threshold Signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Aarhus University, Denmark

    Carmit Hazay & Tomas Toft

  2. The Alexandra Institute, Denmark

    Gert Læssøe Mikkelsen

  3. IBM T.J.Watson Research Center, USA

    Tal Rabin

Authors
  1. Carmit Hazay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gert Læssøe Mikkelsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tal Rabin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tomas Toft
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, University of Haifa, 31905, Haifa, Israel

    Orr Dunkelman

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hazay, C., Mikkelsen, G.L., Rabin, T., Toft, T. (2012). Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting. In: Dunkelman, O. (eds) Topics in Cryptology – CT-RSA 2012. CT-RSA 2012. Lecture Notes in Computer Science, vol 7178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27954-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27954-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27953-9

  • Online ISBN: 978-3-642-27954-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation