In the second chapter, the notion of a social secret sharing (SSS ) scheme is introduced in which shares are allocated based on a player’s reputation and the way she interacts with other parties. In other words, this scheme renews shares at each cycle without changing the secret, and it allows the trusted parties to gain more authority. Our motivation is that, in real-world applications, compon...

Secret sharing is one of the branches of threshold cryptography. Secret sharing is intended to secure a secret key s among a group G with n participants. Thus, the secret key s can be reconstructed by collecting shares of t or more participants. Recently, the secret sharing concept has been applied in securing DNSsec root key. However, the idea of DNSsec root key security is based on Shamir’s (...

We consider the class of secret sharing schemes where there is no a priori bound on the number of players n but where each of the n share-spaces has xed cardinality q. We show two fundamental lower bounds on the threshold gap of such schemes. The threshold gap g is de ned as r − t, where r is minimal and t is maximal such that the following holds: for a secret with arbitrary a priori distributi...

We propose deceptive secret sharing, which is a novel approach to provide both confidentiality and deception in distributed storage systems. The motivation for this is to protect confidentiality as far as possible while acknowledging that no confidentiality scheme provides perfect protection. If confidentiality is breached and information is accessed by unauthorized individuals, our deceptive s...

LDPC codes, LT codes, and digital fountain techniques have received significant attention from both academics and industry in the past few years. By employing the underlying ideas of efficient Belief Propagation (BP) decoding process in LDPC and LT codes, this paper introduces three classes of secret sharing schemes called BP-XOR secret sharing schemes, pseudo-BP-XOR secret sharing schemes, and...

In a group-oriented threshold cryptosystem, each group, instead of each individual member within the group, publishes a single group public key. An outsider can use this group public key to send encrypted messages to the group. However, the received encrypted messages can only be decrypted properly when the number of participating members is larger than or equal to the threshold value. All earl...

In this paper we combine the compartmented secret sharing schemes based on the Chinese remainder theorem with the RSA scheme in order to obtain, as a novelty, a dedicated solution for compartmented threshold decryption or compartmented threshold digital signature generation. AMS Subject Classification: 94A60, 94A62, 11A07

We define three privacy-preserving solutions to the problem of distributing secrets between manufacturers and vendors of items labeled with Electronic Product Code (EPC) Gen2 tags. The solutions rely on the use of an anonymous threshold secret sharing scheme that allows the exchange of blinded information between readers and tags. Moreover, our secret sharing scheme allows self-renewal of share...

In a (r, n)-threshold secret sharing scheme, no group of (r − 1) colluding members can recover the secret value s. However, the number of colluders is likely to increase over time. In order to deal with this issue, one may also require to have the ability to increase the threshold value from r to r′(> r), such an increment is likely to happen several times. In this paper, we study the problem o...