Abstract: Let S be a pool of s parties and Alice be the dealer. In this paper, we propose a scheme that allows the dealer to encrypt messages in such a way that only one authorized coalition of parties (which the dealer chooses depending on the message) can decrypt. At the setup stage, each of the parties involved in the process receives an individual key from the dealer. To decrypt information, an authorized coalition of parties must work together to use their keys. Based on this scheme, we propose a threshold encryption scheme. For a given message f the dealer can choose any threshold m = m(f)More precisely, any set of parties of size at least m can evaluate f; any set of size less than m cannot do this. Similarly, the distribution of keys among the included parties can be done in such a way that authorized coalitions of parties will be given the opportunity to put a collective digital signature on any documents. This primitive can be generalized to the dynamic setting, where any user can dynamically join the pool S. In this case the new user receives a key from the dealer. Also any user can leave the pool S. In both cases, already distributed keys of other users do not change. The main feature of the proposed schemes is that for a given s the keys are distributed once and can be used multiple times. This property distinguishes the proposed schemes from the most of such schemes known in the literature. However, it should be noted that similar schemes have already been proposed (see, for example, the schemes by M. Bellare, A. Boldyreva, K. Kurosawa, J. Staddon (2007) and schemes by C. Delerablee and D. Pointcheval (2008)). The proposed scheme is based on the idea of hidden multipliers in encryption. As a platform, one can use both multiplicative groups of nite elds and groups of invertible elements of commutative rings, in particular, multiplicative groups of residue rings. We propose two versions of this scheme.

Cite: Roman'kov V.
Multi-recipient and threshold encryption based on hidden multipliers
Groups, Complexity, Cryptology. 2022. Т.14. №2. С.3:1–3:12. DOI: 10.46298/jgcc.2022.14.2.10150 WOS

Dates:

Submitted:	Oct 14, 2022
Accepted:	Feb 10, 2023
Published online:	Feb 16, 2023

Identifiers:

Web of science:

WOS:000952324000001

Citing: Пока нет цитирований

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