SHARING A SECRET VIA LINEAR INTERPOLATION
First Claim
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1. A computer-implemented method for distributing a secret, the method comprising:
- forming a linear equation using the secret and random elements, the linear equation representing a K-dimensional secret hyperplane, wherein K is the number of shares to reconstruct the secret;
forming the shares of the secret, with each share containing a point on the secret hyperplane; and
distributing the shares to a plurality of cooperating entities for secret sharing.
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Abstract
A method and system distributes shares of a secret among cooperating entities using linear interpolation. In one embodiment, a linear equation is formed using the secret and random elements. The linear equation represents a K-dimensional secret hyperplane, where K is the number of shares to reconstruct the secret. Shares of the secrets are created, with each share containing a point on the secret hyperplane. The shares are then distributed to cooperating entities for secret sharing.
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Citations
20 Claims
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1. A computer-implemented method for distributing a secret, the method comprising:
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forming a linear equation using the secret and random elements, the linear equation representing a K-dimensional secret hyperplane, wherein K is the number of shares to reconstruct the secret; forming the shares of the secret, with each share containing a point on the secret hyperplane; and distributing the shares to a plurality of cooperating entities for secret sharing. - View Dependent Claims (2, 3, 4, 5)
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6. A system for dividing a secret into a plurality of shares, the system comprising:
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data storage to store the secret; and a computing entity coupled to the data storage to generate the shares of the secret for distribution among cooperating entities, the computing entity comprising; a random value generator to generate random values; and a share generator to use the secret and the random values to form a linear equation that represents a K-dimensional secret hyperplane, and to create the shares of the secret with each share containing a point on the secret hyperplane, wherein K is the number of the shares to reconstruct the secret. - View Dependent Claims (7, 8, 9)
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10. A computer readable storage medium including instructions that, when executed by a processing system, cause the processing system to perform a method comprising:
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forming a linear equation using the secret and random elements, the linear equation representing a K-dimensional secret hyperplane, wherein K is the number of shares to reconstruct the secret; forming the shares of the secret, with each share containing a point on the secret hyperplane; and distributing the shares to a plurality of cooperating entities for secret sharing. - View Dependent Claims (11, 12, 13, 14)
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15. A computer-implemented method for reconstructing a secret, the method comprising:
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collecting K shares of the secret from cooperating entities, wherein K is the number of shares to reconstruct the secret; constructing K linear equations with K unknowns using the K shares, the linear equations defining a K-dimensional secret hyperplane on which the secret is embedded; reconstructing the secret hyperplane by solving for the K unknowns; and extracting the secret from the secret hyperplane. - View Dependent Claims (16, 17)
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18. A system for reconstructing a secret, the system comprising:
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a receiving interface to collect K shares of the secret from cooperating entities, wherein K is the number of shares to reconstruct the secret; and a linear operator coupled to the receiving interface to use the K shares to construct K linear equations with K unknowns, the linear equations to define a K-dimensional secret hyperplane on which the secret is embedded, the linear operator to reconstruct the secret hyperplane with solved K unknowns and to extract the secret from the secret hyperplane. - View Dependent Claims (19, 20)
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Specification