Multisecret-sharing schemes and bounded distance decoding of linear codes

ABSTRACT

Error-correcting codes are used to correct errors when messages are transmitted through a noisy communication channel. Bounded distance decoding (i.e. decoding up to the error-correcting capacity) is a method of correcting errors that guarantees unique decoding. Secret sharing is a cryptographic protocol that allows a secret known from a person called the dealer to be distributed to n participants. No single participant knows the secret but some special subsets of participants called coalitions can. In this paper, we present a multisecret-sharing scheme based on an error-correcting code where secret reconstruction is made by using bounded distance decoding of the code. This scheme is ideal in the sense that the size of each secret equals the size of any share. Its security improves on that of multisecret-sharing schemes.

KEYWORDS:

• Secret sharing
• multisecret-sharing
• ideal secret sharing
• bounded distance decoding
• linear code

2010 AMS SUBJECT CLASSIFICATIONS:

• 94B35
• 94A60

Disclosure statement

No potential conflict of interest was reported by the authors.