Study On Verifiable Secret Sharing Scheme

Key management is one of the important cryptographic problems. Linear threshold scheme and visual cryptography scheme provide two different methods to solve problem of secret sharing. This dissertation devotes to the related problems of secret sharing and the main contributions are listed as follows:(1) While the dealer is not on-line in a (k, n)-threshold scheme, assume t(t≥1) new participants want to share the secret, there exists a problem to distribute shares to new participants. This paper adopts the (k,n+t) scheme transformed from old (k,n) scheme based on Lagrange interpolation in which k out of n old participants will function as the dealer to distribute new shares to t new participants. The scheme achieves the distribution of searet to t new participants. k out of n+t shares can reconstruct the secret and less than k shares will get no information about the secret.(2) Typical publicly verifiable secret sharing schemes rely on a dealer to distribute shares. However, there may be cheating action from the dealer which distributes an inconsistent secret to participants. In order to prevent cheating action from the dealer, two publicly verifiable secret sharing are presented based on the Chinese Remainder Theorem and Lagrange interpolation separately without the dealer substituded by n participants to jointly generate shared secret and to distribute their shares. ElGamal cryptosystem is used to encrypt transmitted information. The public verification is realized by utilizing zero-knowledge proof.(3) Existing multi-threshold multi-secret sharing schemes need private channel to transmit information. Their shares can not be selected by the dealer instead of participants. The verification can not preventing the cheating action from the dealer distributing an inconsistent secret to participants. Because of the high cost to protect private channel, an improved scheme is proposed in this paper. The information is encrypted using the RSA cryptosystem so that the public channels can be used to transmit data and participants can choose their shares by themselves in the proposed scheme. The new scheme is provided with verification which ulilizes exponentional opreations among the dealer, participants and secrets combiner.(4) Visual secret sharing scheme has disadvantage of pixel expansion since each original pixel is encoded into m subpixels per shadow image. Probabilistic visual secret sharing scheme uses the frequency of white pixels in the black and white areas of the recoverd image for interpreting black and white pixels by human visual system to present non-expansible scheme. We propose a new method to reduce the pixel expansion based on image shrinking algorithm. The main problem of the shrinking algorithm is how to preserve the shape and topology of the image during the shrinking. We propose two image shrinking algorithms to preserve shape and topology utilizing human visual system and connectivity classification.