| A secret sharing scheme creates an effective method to safeguard a secret by dividing it among several participants. Since the original idea introduced by Shamir and Blakley in 1979, a variety of threshold secret sharing schemes and other types have been suggested by researchers. The first part of this thesis shows how to apply hash functions in secret sharing scheme designs. By using hash functions and the herding hashes technique, we first set up a (t + 1, n) threshold scheme which is perfect and ideal, and then extend it to schemes for any general access structure. The schemes can be further set up as verifiable if necessary. The secret can be quickly recovered due to the fast calculation of the hash function. In particular, secret sharing schemes based on Latin squares will be discussed.;The practical hash functions used today, such as SHA-1 and SHA-2 families, are iterative hash functions. Although there are many suggestions to improve the security of an iterative hash function, the general idea of processing the message block by block still enables many attacks, which make use of the intermediate hash values, possible. The second part of this thesis proposes a new hash function construction scheme that applies the randomize-then-combine technique, which was used in the incremental hash functions, to the iterative hash construction to prevent those attacks. |
