EFFICIENT VERIFIABLE SECRET SHARING SCHEME USING RSA CRYPTOGRAPHY

Abstract

Authenticity is one of the key aspects of security. As a cryptographic technique that guarantees information authenticity, secret sharing has been an active research field for many years. With the efforts of pioneering researchers, secret sharing has reached the level of practical application use in today's environment, which is designed to protect a secret piece of information among a group of users in such a way that only certain subsets of users can jointly reconstruct the secret whereas other subsets of users can ideally not obtain any information about the secret. Splitting the secret ensures that no has the complete the secret. Also, as all shares are of the same length, it makes guessing impossible. A well-known principle in the world is "reduced trust”, i.e. in order to maintain any secret, lesser the power or knowledge an entity have, greater are the chances of keeping that secret. This philosophy is implemented in the digital world as well. Thus the idea of verifiability was introduced in the secret sharing as well. Although there are several other means to check the verifiability of the shares, in this project, the pioneer secret sharing scheme authored by Adi Shamir is studied for verifiable secret sharing (VSS) using RSA. In this verifiable secret sharing scheme (VSSS), the secret is shared among the set of participants after signing the shares with their private key, such that only specific subsets of the participants, after verifying their shares with the public keys, can successfully recover the secret at a later time using their private keys. Both Shamir’s secret sharing scheme and RSA are unconditionally secure for both the secret as well the shares; together they complement each other in the VSSS.