Abstract
In 1979, Blackley and Shamir independently proposed schemes by which a secret can be divided into many shares which can be distributed to mutually suspicious agents. This paper describes a homomorphism property attained by these and several other secret sharing schemes which allows multiple secrets to be combined by direct computation on shares. This property reduces the need for trust among agents and allows secret sharing to be applied to many new problems. One application described here gives a method of verifiable secret sharing which is much simpler and more efficient than previous schemes. A second application is described which gives a fault-tolerant method of holding verifiable secret-ballot elections.
This work was supported in part by the National Security Agency under Grant MDA904-84-H-0004.
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Adleman, L. “Subexponential Algorithm for The Discrete Logarithm Problem.” Proc. 20thIEEE Symp. on Foundations of Computer Science, San Juan, PR (Oct. 1979), 55–60.
Asmuth, C. and Bloom, J. “A Modular Approach to Key Safeguarding.” Texas A&M University, Departement of Mathematics, College Station, TX (1980).
Benaloh, J. and Yung, M. “Distributing the Power of a Government to Enhance the Privacy of Voters.” Proc. 5thACM Symp. on Principles of Distributed Computing, Calgary, AB (Aug. 1986).
Blakley, G. “Safeguarding Cryptographic Keys.” Proc. AFIPS 1979 National Computer Conference, New York, NY (June 1979), 313–317.
Blakley, G. and Meadows, C. “A Database Encryption Scheme Which Allows the Computation of Statistics Using Encrypted Data.” Proc. IEEE Symposium on Computer Security and Privacy, Oakland, CA (Apr. 1985).
Chor, B., Goldwasser, S., Micali, S., and Awerbuch, B. “Verifiable Secret Sharing and Achieving Simultaneity in the Presence of Faults.” Proc. 26thIEEE Symp. on Foundations of Computer Science, Portland, OR (Oct. 1985), 383–395.
Cohen, J. and Fischer, M. “A Robust and Verifiable Cryptographically Secure Election Scheme.” Proc. 26thIEEE Symp. on Foundations of Computer Science, Portland, OR (Oct. 1985), 372–382.
Cohen, J. “Improving Privacy in Cryptographic Elections.” TR-454, Yale University, Departement of Computer Science, New Haven, CT (Feb. 1986).
Coppersmith, D., Odlyzko, A., and Schroeppel, R. “Discrete Logarithms in GF(p).” Algorithmica, 1 (1986), 1–15.
DeMillo, R., Lynch, N., and Merritt, M. “Cryptographic Protocols.” Proc. 14thACM Symp. on Theory of Computing, San Francisco, CA (May 1982), 383–400.
Feigenbaum, J. “Encrypting Problem Instances or Can You Take Advantage of Someone Without Having to Trust Him”, Proc. Crypto’ 85, Santa Barbara, CA (Aug. 1985), 477–488. Published as Advances in Cryptology, ed. by H. Williams in Lecture Notes in Computer Science, vol. 218, ed. by G. Goos and J. Hartmanis. Springer-Verlag, New York (1985).
Fischer, M., Micali, S., and Rackoff, C. “A Secure Protocol for the Oblivious Transfer.” Presented at Eurocrypt84, Paris, France (Apr. 1984). (Not in proceedings.)
Goldwasser, S., Micali, S., and Rackoff C. “The Knowledge of Complexity of Interactive Proof-Systems.” Proc. 17thACM Symp. on Theory of Computing, Providence, RI (May 1985), 291–304.
Goldwasser, S. and Micali, S. “Probabilistic Encryption.” J. Comput. System Sci. 28, (1984), 270–299.
Kothari, S. “Generalized Linear Threshold Scheme.” Proc. Crypto’ 84, Santa Barbara, CA (Aug. 1984), 231–241. Published as Advances in Cryptology, ed. by G. Blakely and D. Chaum in Lecture Notes in Computer Science, vol. 196, ed. by G. Goos and J. Hartmanis. Springer-Verlag, New York (1985).
Pohlig, S. and Hellman, M. “An Improved Algorithm for Computing Logarithms Over GF(2) and Its Cryptographic Significance.” IEEE Trans. on Information Theory 24,1 (Jan. 1978), 106–110.
Rivest, R., Adleman, L., and Dertouzos, M. “On Data Banks and Privacy Homomorphisms.” Foundations of Secure Computation, ed. by R. A. DeMillo, et al. Academic Press, New York (1978), 169–179.
Shamir, A. “How to Share a Secret.” Comm. ACM 22, 11 (Nov. 1979), 612–613.
Yao, A. “Protocols for Secure Computations.” Proc. 23rdIEEE Symp. on Foundations of Computer Science, Chicago, IL (Nov. 1982), 160–164.
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Benaloh, J.C. (1987). Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret (Extended Abstract). In: Odlyzko, A.M. (eds) Advances in Cryptology — CRYPTO’ 86. CRYPTO 1986. Lecture Notes in Computer Science, vol 263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47721-7_19
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