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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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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