The Secure Hash Algorithm (SHA), the algorithm specified in the Secure Hash Standard (SHS), was developed by NIST and published as a federal information processing standard (FIPS PUB 180). SHA-1 was a revision to SHA that was published in 1994. The revision corrected an unpublished flaw in SHA. Its design is very similar to the MD4 family of hash functions developed by Rivest.
For a brief overview here, we note that hash functions are often divided into three classes according to their design:
those built around block ciphers,
those which use modular arithmetic, and
those which have what is termed a "dedicated" design.
By building a hash function around a block cipher, it is intended that by using a well-trusted block cipher such as DES a secure and well-trusted hash function can be obtained. The so-called Davies-Meyer hash function is an example of a hash function built around the use of DES.
A message authentication code (MAC) is an authentication tag (also called a checksum) derived by application of an authentication scheme, together with a secret key, to a message. MACs are computed and verified with the same key so they can only be verified by the intended receiver, unlike digital signatures. MACs can be categorized as (1) unconditionally secure, (2) hash function-based, (3) stream cipher-based, or (4) block cipher-based.
Simmons and Stinson proposed an unconditionally secure MAC that is based on encryption with a one-time pad. The ciphertext of the message authenticates itself, as nobody else has access to the one-time pad. However, there has to be some redundancy in the message. An unconditionally secure MAC can also be obtained by use of a one-time secret key.
Shamir's secret sharing scheme is an interpolating scheme based on polynomial interpolation. An (m - 1)-degree polynomial over the finite field GF(q)
Blakley's secret sharing scheme is geometric in nature. The secret is a point in an m-dimensional space. n shares are constructed with each share defining a hyperplane in this space. By finding the intersection of any m of these planes, the secret (or point of intersection) can be obtained. This scheme is not perfect, as the person with a share of the secret knows that the secret is a point on his hyperplane. Nevertheless, this scheme can be modified to achieve perfect security.This is based on the scenario where two shares are required to recover the secret. A two-dimensional plane is used as only two shares are required to recover the secret. The secret is a point in the plane. Each share is a line that passes through the point. If any two of the shares are put together, the point of intersection, which is the secret, can be easily derived.