Abstract-Key transfer protocols rely on a mutually trusted key generation center (KGC) to select session keys and transport session keys to all communication entities secretly. Most often, KGC encrypts session keys under another secret key shared with each entity during registration. In this paper, we propose an authenticated key transfer protocol based on secret sharing scheme that KGC can broadcast group key information to all group members at once and only authorized group members can recover the group key; but unauthorized users cannot recover the group key. The confidentiality of this transformation is information theoretically secure. We also provide authentication for transporting this group key. Goals and security threats of our proposed group key transfer protocol will be analyzed in detail.
In a (t, n) secret sharing scheme, a secret s is divided into n shares and shared among a set of n shareholders by a mutually trusted dealer in such a way that any t or more than t shares will be able to reconstruct this secret; but fewer than t shares cannot know any information about the secret. When shareholders present their shares in the secret reconstruction phase, dishonest shareholder(s) (i.e. cheater(s)) can always exclusively derive the secret by presenting faked share(s) and thus the other honest shareholders get nothing but a faked secret. Cheater detection and identification are very important to achieve fair reconstruction of a secret. In this paper, we consider the situation that there are more than t shareholders participated in the secret reconstruction. Since there are more than t shares (i.e. it only requires t shares) for reconstructing the secret, the redundant shares can be used for cheater detection and identification. Our proposed scheme uses the shares generated by the dealer to reconstruct the secret and, at the same time, to detect and identify cheaters. We have included discussion on three attacks of cheaters and bounds of detectability and identifiability of our proposed scheme under these three attacks. Our proposed scheme is an extension of Shamir's secret sharing scheme. Communicated by P. Wild.
In Shamir's (t, n) secret sharing (SS) scheme, the secret s is divided into n shares by a dealer and is shared among n shareholders in such a way that any t or more than t shares can reconstruct this secret; but fewer than t shares cannot obtain any information about the secret s. In this paper, we will introduce the security problem that an adversary can obtain the secret when there are more than t participants in Shamir's secret reconstruction. A secure secret reconstruction scheme, which prevents the adversary from obtaining the secret is proposed. In our scheme, Lagrange components, which are linear combination of shares, are used to reconstruct the secret. Lagrange component can protect shares unconditionally. We show that this scheme can be extended to design a multi-secret sharing scheme. All existing multi-secret sharing schemes are based on some cryptographic assumptions, such as a secure one-way function or solving the discrete logarithm problem; but, our proposed multi-secret sharing scheme is unconditionally secure.
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