System for reconstruction of a secret shared by a plurality of participants
First Claim
1. A method for reconstructing a secret, over a public communication channel, using a perfect t-out-of-n secret sharing scheme;
- the t-out-of-n secret sharing scheme having a dealer which utilizes a delivering procedure for privately delivering n secret shares of said secret along with n keys to respective n participants that are interlinked by said public communication channel;
the key that is delivered to each one of said n participants is composed of, or is serving for generating n-1 key constituents for respectively communicating, over said public communication channel, with the remaining n-1 participants from among said n participants;
said secret sharing scheme further having a secret reconstructing procedure for being executed by each one of at least one recipient participant selected from a group of l participants from among said n participants, for reconstructing said secret by utilizing self secret share of said recipient participant and l-1 secret shares of the remaining l-1 participants from among said l participants;
said secret reconstructing procedure, executed by each one of said recipient participants, comprising the following steps;
(i) receiving over said public communication channel l-1 encoded secret shares from the l-1 participants, respectively;
the l-1 encoded secret shares being generated, each, by one and different participant from among said l-1 participants, by applying an encoding function which utilizes a key constituent from among said n-1 key constituents that is adapted for communicating between said one participant and said recipient participant;
(ii) decoding each one of said l-1 encoded secret shares, thereby obtaining l-1 decoded secret shares;
the l-1 decoded secret share are obtained, each, by applying a decoding function that utilizes said key constituent, stipulated in step (i), that is adapted for communication between said one participant and said recipient participant; and
(iii) reconstructing said secret from the l-1 decoded secret shares and from the self secret share of the recipient participant.
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Abstract
A method for reconstructing a secret, over a public communication channel, using a perfect t-out-of-n secret sharing scheme. The scheme having a dealer which utilizes a delivering procedure for privately delivering n secret shares of the secret along with n keys to n participants that are interlinked by the channel. The scheme further having a secret reconstructing procedure for being executed by selected recipient participants, for reconstructing the secret by utilizing self secret share of the recipient participant and l-1 secret shares of the other participants. The secret reconstructing procedure includes the following steps:
(i) receiving over said public communication channel l-1 encoded secret shares from the l-1 participants, respectively;
(ii) decoding each one of the l-1 encoded secret shares, thereby obtaining l-1 decoded secret shares; and
(iii) reconstructing the secret from the l-1 decoded secret shares and from the self secret share of the recipient participant.
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Citations
43 Claims
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1. A method for reconstructing a secret, over a public communication channel, using a perfect t-out-of-n secret sharing scheme;
- the t-out-of-n secret sharing scheme having a dealer which utilizes a delivering procedure for privately delivering n secret shares of said secret along with n keys to respective n participants that are interlinked by said public communication channel;
the key that is delivered to each one of said n participants is composed of, or is serving for generating n-1 key constituents for respectively communicating, over said public communication channel, with the remaining n-1 participants from among said n participants;said secret sharing scheme further having a secret reconstructing procedure for being executed by each one of at least one recipient participant selected from a group of l participants from among said n participants, for reconstructing said secret by utilizing self secret share of said recipient participant and l-1 secret shares of the remaining l-1 participants from among said l participants; said secret reconstructing procedure, executed by each one of said recipient participants, comprising the following steps; (i) receiving over said public communication channel l-1 encoded secret shares from the l-1 participants, respectively;
the l-1 encoded secret shares being generated, each, by one and different participant from among said l-1 participants, by applying an encoding function which utilizes a key constituent from among said n-1 key constituents that is adapted for communicating between said one participant and said recipient participant;(ii) decoding each one of said l-1 encoded secret shares, thereby obtaining l-1 decoded secret shares;
the l-1 decoded secret share are obtained, each, by applying a decoding function that utilizes said key constituent, stipulated in step (i), that is adapted for communication between said one participant and said recipient participant; and(iii) reconstructing said secret from the l-1 decoded secret shares and from the self secret share of the recipient participant. - View Dependent Claims (2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27)
- the t-out-of-n secret sharing scheme having a dealer which utilizes a delivering procedure for privately delivering n secret shares of said secret along with n keys to respective n participants that are interlinked by said public communication channel;
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8. A method for reconstructing a secret, over a public communication channel, using a perfect t-out-of-n secret sharing scheme;
- the t-out-of-n secret sharing scheme having a dealer capable of partitioning said secret to t sub-secrets each of which being subjected to a delivering procedure for privately delivering n sub secret shares thereof to respective n participants that are interlinked by said public communication channel;
said dealer is further capable of privately delivering n keys to the respective n participants;
the key that is delivered to each one of said n participants is composed of, or is serving for generating, n-1 key constituents for respectively communicating, over said public communication channel, with the remaining n-1 participants from among said n participants;said secret sharing scheme further having a secret reconstructing procedure for being executed by each one of l participants (l≧
t), constituting, respectively, l recipient participants, from among said n participants, for reconstructing said secret by utilizing a self secret share of said recipient participant and l-1 secret shares of the remaining l-1 participants from among said l participants;said secret reconstructing procedure, executed by each one of t participants from among said l recipient participants, comprising the following steps; (i) receiving over said public communication channel t-1 encoded sub secret shares from the remaining t-1 participants, from among said t participants;
the t-1 encoded sub secret shares being generated, each, by one and different participant from among said t-1 participants, by applying to said sub secret share an encoding function which utilizes a key constituent from among said n-1 key constituents that is adapted for communicating between said one participant and said recipient participant;(ii) decoding each one of said t-1 encoded sub secret shares, thereby obtaining t-1 decoded sub secret shares;
the t-1 decoded sub secret shares are obtained, each, by applying thereto a decoding function that utilizes said key constituent, stipulated in step (i), that is adapted for communication between said one participant and said recipient participant;(iii) reconstructing said sub secret from the t-1 decoded sub secret shares and from the sub secret share of the recipient participant;
said secret reconstructing procedure, further comprising the steps(iv)-(vi), executed by each one of said I recipient participants; (iv) receiving over said public communication channel t or t-1 encoded sub secrets from said t or t-1 participants, respectively;
the t or t-1 encoded sub secrets being generated, each, by one and different participant from among said t or t-1 participants, by applying to said sub secret an encoding function which utilizes a key constituent from among said n-1 key constituents that is adapted for communicating between said one participant and said recipient participant;(v) decoding each one of said t or t-1 encoded sub secrets so as to obtain t or t-1 decoded sub secrets;
the t or t-1 decoded sub secrets are obtained, each, by applying thereto a decoding function that utilizes said key constituent, stipulated in step (iv), that is adapted for communication between said one participant and said recipient participant, thereby accomplishing t sub secrets; and(vi) reconstructing said secret from the t sub secrets. - View Dependent Claims (9, 10, 11, 20, 24, 28)
- the t-out-of-n secret sharing scheme having a dealer capable of partitioning said secret to t sub-secrets each of which being subjected to a delivering procedure for privately delivering n sub secret shares thereof to respective n participants that are interlinked by said public communication channel;
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29. A system for reconstructing a secret, over a public communication channel, using a perfect t-out-of-n secret sharing scheme;
- the t-out-of-n secret sharing scheme having a dealing means for privately dealing n secret shares of said secret along with n keys to respective n participants interlinked by said public communication channel;
for each participant, the key that is dealt thereto is composed of, or is associated with generating means for generating n-1 key constituents for respectively communicating, over said public communication channel, with the remaining n-1 participants from among said n participants;said secret sharing scheme further having a secret reconstructing means associated with each of at least one recipient participant selected from a group of l participants from among said n participants, for reconstructing said secret by utilizing self secret share of said recipient participant and l-1 secret shares of the remaining l-1 participants from among said l participants; said secret reconstructing means associated with each of said at least one recipient participant is capable of; (i) receiving over said public communication channel l-1 encoded secret shares from the l-1 participants, respectively;
the l-1 encoded secret shares being generated, each, by one and different participant from among said l-1 participants, by applying an encoding function which utilizes a key constituent from among said n-1 key constituents that is adapted for communicating between said one participant and said recipient participant;(ii) decoding each one of said l-1 encoded secret shares, thereby obtaining l-1 decoded secret shares;
the l-1 decoded secret share are obtained, each, by applying a decoding function that utilizes said key constituent, stipulated in step (i), that is adapted for communication between said one participant and said recipient participant; and(iii) reconstructing said secret from the l-1 decoded secret shares and from the self secret share of the recipient participant. - View Dependent Claims (30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43)
- the t-out-of-n secret sharing scheme having a dealing means for privately dealing n secret shares of said secret along with n keys to respective n participants interlinked by said public communication channel;
Specification