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Threshold cryptosystems

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Book cover Advances in Cryptology — AUSCRYPT '92 (AUSCRYPT 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 718))

Abstract

Often the power to use a cryptosystem has to be shared. In threshold schemes, t-out-of-l have the power to regenerate a secret key (while less than t have not). However threshold schemes cannot be used directly in many applications, such as threshold signatures in which t-out-of-l have to co-sign a message. A normal threshold scheme would require the shareholders to send their shares to a trusted person who would sign for them. But the use of such a trusted person violates the main point of threshold signatures!

We first overview the research in the field and then discuss a threshold decryption/signature scheme which is as secure as RSA. We conclude by giving a list of open problems.

A part of this work has been supported by NSF Grant NCR-9106327.

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References

  1. Benaloh, J. C.: Secret sharing homomorphisms: Keeping shares of a secret secret. In Advances in Cryptology, Proc. of Crypto '86 (Lecture Notes in Computer Science 263) (1987) A. Odlyzko, Ed. Springer-Verlag pp. 251–260

    Google Scholar 

  2. Blakley, G. R.: Safeguarding cryptographic keys. In Proc. Nat. Computer Conf. AFIPS Conf. Proc. (1979) pp. 313–317

    Google Scholar 

  3. Boyd, C.: Digital multisignatures. In Cryptography and coding (1989) H. Beker and F. Piper, Eds. Clarendon Press pp. 241–246

    Google Scholar 

  4. Burmester, M. V. D., Desmedt, Y. G., Piper, F., Walker, M.: A general zeroknowledge scheme. In Advances in Cryptology, Proc. of Eurocrypt '89 (Lecture Notes in Computer Science 434) (1990) J.-J. Quisquater and J. Vandewalle, Eds. Springer-Verlag pp. 122–133

    Google Scholar 

  5. Cerecedo, M., Matsumoto, T., Imai, H.: Non-interactive generation of shared pseudorandom sequences. Presented at Auscrypt'92, Mudgeeraba, Queensland, Australia, to appear in the proceedings (Lecture Notes in Computer Science), Springer-Verlag December 13–16, 1992

    Google Scholar 

  6. Chaum, D., van Antwerpen, H.: Undeniable signatures. In Advances in Cryptology — Crypto '89, Proceedings (Lecture Notes in Computer Science 435) (1990) G. Brassard, Ed. Springer-Verlag pp. 212–216

    Google Scholar 

  7. Chaum, D., van Heyst, E.: Group signatures. In Advances in Cryptology, Proc. of Eurocrypt '91 (Lecture Notes in Computer Science 547) (April 1991) D. W. Davies, Ed. Springer-Verlag pp. 257–265

    Google Scholar 

  8. Croft, R. A., Harris, S. P.: Public-key cryptography and re-usable shared secrets. In Cryptography and coding (1989) H. Beker and F. Piper, Eds. Clarendon Press pp. 189–201

    Google Scholar 

  9. De Santis, A., Desmedt, Y., Frankel, Y., Yung, M.: Quorum cryptography and non-interactive protocols. In preparation (Available from authors when completed)

    Google Scholar 

  10. De Soete, M., Quisquater, J.-J., Vedder, K.: A signature with shared verification scheme. In Advances in Cryptology — Crypto '89, Proceedings (Lecture Notes in Computer Science 435) (1990) G. Brassard, Ed. Springer-Verlag pp. 253–262

    Google Scholar 

  11. Denning, D. E.: Panel: Digital telephony October 13–16, 1992. National Computer Security Conference, Baltimore

    Google Scholar 

  12. Desmedt, Y.: Threshold cryptography. Invited paper, to be presented at SPRC '93, 3rd Symposium on State and Progress of Research in Cryptography, Roma, Italy February 15–16, 1993

    Google Scholar 

  13. Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In Advances in Cryptology — Crypto '89, Proceedings (Lecture Notes in Computer Science 435) (1990) G. Brassard, Ed. Springer-Verlag pp. 307–315

    Google Scholar 

  14. Desmedt, Y., Frankel, Y.: Shared generation of authenticators and signatures. In Advances in Cryptology — Crypto '91, Proceedings (Lecture Notes in Computer Science 576) (1992) J. Feigenbaum, Ed. Springer-Verlag pp. 457–469

    Google Scholar 

  15. Desmedt, Y. G.: Abuse-free cryptosystems: Particularly subliminal-free authentication and signature. Submitted to the Journal of Cryptology, under revision April 1989

    Google Scholar 

  16. Desmedt, Y.: Society and group oriented cryptography: a new concept. In Advances in Cryptology, Proc. of Crypto '87 (Lecture Notes in Computer Science 293) (1988) C. Pomerance, Ed. Springer-Verlag pp. 120–127

    Google Scholar 

  17. Desmedt, Y., Frankel, Y.: Perfect zero-knowledge sharing schemes over any finite Abelian group. Presented at Sequences '91, June 17–22, 1991, Positano, Italy, to appear in: the Proceedings, Springer-Verlag 1991

    Google Scholar 

  18. Desmedt, Y., Frankel, Y., Yung, M.: Multi-receiver/multi-sender network security: efficient authenticated multicast/feedback. In IEEE INFOCOM '92, Eleventh Annual Joint Conference of the IEEE Computer and Communications Societies (Florence, Italy, May 4–8, 1992) pp. 2045–2054

    Google Scholar 

  19. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inform. Theory 31 (1985) 469–472

    Google Scholar 

  20. Frankel, Y.: A practical protocol for large group oriented networks. In Advances in Cryptology, Proc. of Eurocrypt '89 (Lecture Notes in Computer Science 434) (1990) J.-J. Quisquater and J. Vandewalle, Eds. Springer-Verlag pp. 56–61

    Google Scholar 

  21. Frankel, Y., Desmedt, Y.: Parallel reliable threshold multisignature. Tech. Report TR-92-04-02 Dept. of EE & CS, Univ. of Wisconsin-Milwaukee April 1992. Submitted to ACM Transactions on Computer Systems with title: Distributed reliable threshold multisignatures

    Google Scholar 

  22. Frankel, Y., Desmedt, Y.: Classification of ideal homomorphic threshold schemes over finite Abelian groups. Presented at Eurocrypt '92, Balatonfüred, Hungary, to appear in Advances in Cryptology, Proc. of Eurocrypt '92, (Lecture Notes in Computer Science), Springer-Verlag May 24–28, 1992

    Google Scholar 

  23. Franklin, M., Yung, M.: Varieties of secure distributed computing. Presented at the Second Advanced Workshop on Sequences: Combinatorics, Compression, Security and Transmission, June 17–22, 1991, Positano, Italy, to appear in: Sequences, Springer-Verlag

    Google Scholar 

  24. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In Proceedings of the Nineteenth annual ACM Symp. Theory of Computing, STOC (May 25–27, 1987) pp. 218–229

    Google Scholar 

  25. Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. Siam J. Comput. 18 (1989) 186–208

    Google Scholar 

  26. Goldwasser, S., Micali, S., Rivest, R.: A digital signature scheme secure against adaptive chosen-message attacks. Siam J. Comput. 17 (1988) 281–308

    Google Scholar 

  27. Harn, L., Yang, S.: Group-oriented undeniable signature schemes without the assistance of a mutually trusted party. Presented at Auscrypt'92, Mudgeeraba, Queensland, Australia, to appear in the proceedings (Lecture Notes in Computer Science), Springer-Verlag December 13–16, 1992

    Google Scholar 

  28. Hwang, T.: Cryptosystems for group oriented cryptography. In Advances in Cryptology, Proc. of Eurocrypt '90 (Lecture Notes in Computer Science 473) (1991) I. Damgård, Ed. Springer-Verlag pp. 352–360

    Google Scholar 

  29. Ito, M., Saito, A., Nishizeki, T.: Secret sharing schemes realizing general access structures. In Proc. IEEE Global Telecommunications Conf., Globecom'87 (1987) IEEE Communications Soc. Press pp. 99–102

    Google Scholar 

  30. Laih, C.-S., Harn, L.: Generalized threshold cryptosystems. Presented at Asiacrypt'91, November 11–14, 1991, Fujiyoshida, Yamanashi, Japan, to appear in: Advances in Cryptology. Proc. of Asiacrypt'91 (Lecture Notes in Computer Science), Springer-Verlag

    Google Scholar 

  31. Micali, S.: Fair public-key cryptosystems. Presented at Crypto'92, Santa Barbara, California, U.S.A., to appear in Advances in Cryptology — Crypto '92, Proceedings (Lecture Notes in Computer Science), Springer-Verlag Augustus 16–20, 1992

    Google Scholar 

  32. Ohta, K., Okamoto, T.: A digital multisignature scheme based on the Fiat-Shamir scheme. Presented at Asiacrypt'91, November 11–14, 1991, Fujiyoshida, Yamanashi, Japan, to appear in: Advances in Cryptology. Proc. of Asiacrypt'91 (Lecture Notes in Computer Science), Springer-Verlag 1991

    Google Scholar 

  33. Okamoto, T.: A digital multisignature scheme using bijective public-key cryptosystems. ACM Trans. on Computer Systems 6 (1988) 432–441

    Google Scholar 

  34. Pedersen, T. P.: Distributed provers with applications to undeniable signatures. In Advances in Cryptology, Proc. of Eurocrypt '91 (Lecture Notes in Computer Science 547) (April 1991) D. W. Davies, Ed. Springer-Verlag pp. 221–242

    Google Scholar 

  35. Pedersen, T. P.: A threshold cryptosystem without a trusted party. In Advances in Cryptology, Proc. of Eurocrypt '91 (Lecture Notes in Computer Science 547) (April 1991) D. W. Davies, Ed. Springer-Verlag pp. 522–526

    Google Scholar 

  36. Rivest, R. L., Hellman, M. E., Anderson, J. C.: Responses to NIST's proposal. Commun. ACM 35 (1992) 41–54

    Google Scholar 

  37. Rivest, R. L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Commun. ACM 21 (1978) 294–299

    Google Scholar 

  38. Schnorr, C. P.: Efficient identification and signatures for smart cards. In Advances in Cryptology — Crypto '89, Proceedings (Lecture Notes in Computer Science 435) (1990) G. Brassard, Ed. Springer-Verlag pp. 239–252

    Google Scholar 

  39. Shamir, A.: How to share a secret. Commun. ACM 22 (1979) 612–613

    Google Scholar 

  40. Shannon, C. E.: Communication theory of secrecy systems. Bell System Techn. Jour. 28 (1949) 656–715

    Google Scholar 

  41. Simmons, G. J.: An introduction to shared secret and/or shared control schemes and their application. In Contemporary Cryptology, G. J. Simmons, Ed. IEEE Press 1992 pp. 441–497

    Google Scholar 

  42. Simmons, G. J., Jackson, W., Martin, K.: The geometry of shared secret schemes. Bulletin of the Institute of Combinatorics and its Applications 1 (1991) 71–88

    Google Scholar 

  43. Vernam, G. S.: Cipher printing telegraph systems for secret wire and radio telegraphic communications. Journal American Institute of Electrical Engineers XLV (1926) 109–115

    Google Scholar 

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Authors and Affiliations

  1. EE & CS Department, University of Wisconsin-Milwaukee, 53201, WI, USA

    Yvo Desmedt

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  1. Yvo Desmedt
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Jennifer Seberry Yuliang Zheng

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© 1993 Springer-Verlag Berlin Heidelberg

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Desmedt, Y. (1993). Threshold cryptosystems. In: Seberry, J., Zheng, Y. (eds) Advances in Cryptology — AUSCRYPT '92. AUSCRYPT 1992. Lecture Notes in Computer Science, vol 718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57220-1_47

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  • DOI: https://doi.org/10.1007/3-540-57220-1_47

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  • Print ISBN: 978-3-540-57220-6

  • Online ISBN: 978-3-540-47976-5

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