Lecture 4 part 1

Secure Hash Functions
The one-way hash function, or secure hash function, is important not only in message authentication but in digital signatures. In this lecture, we begin with a discussion of requirements for a secure hash function.

HASH FUNCTION REQUIREMENTS The purpose of a hash function is to produce a “fingerprint” of a file, message, or other block of data. To be useful for message authentication, a hash function H must have the following properties:
1. H can be applied to a block of data of any size.
2. H produces a fixed-length output.
3. H(x) is relatively easy to compute for any given x, making both hardware and software implementations practical.
4. For any given code h, it is computationally infeasible to find x such that
H(x) = h. A hash function with this property is referred to as one-way or preimage
resistant .
5. For any given block x, it is computationally infeasible to find y ? x with
H(y) = H(x). A hash function with this property is referred to as second preimage resistant . This is sometimes referred to as weak collision resistant .

The first three properties are requirements for the practical application of a hash function to message authentication.
The fourth property is the one-way property: It is easy to generate a code given a message, but virtually impossible to generate a message given a code.
The fifth property guarantees that it is impossible to find an alternative message with the same hash value as a given message.

SECURE HASH FUNCTION ALGORITHMS In recent years, the most widely used hash function has been the Secure Hash Algorithm (SHA). SHA was developed by the National Institute of Standards and Technology (NIST) and published as a federal information processing standard (FIPS 180) in 1993.


CIPHER BLOCK MODES OF OPERATION
A symmetric block cipher processes one block of data at a time. In the case of DES and 3DES, the block length is 64 bits. For longer amounts of plaintext, it is necessary to break the plaintext into 64-bit blocks (padding the last block if necessary).
To apply a block cipher in a variety of applications, five modes of operation have been defined by NIST (Special Publication 800-38A). The five modes are proposed to cover virtually all the possible applications of encryption for which a block cipher could be used.
These modes are proposed for use with any symmetric block cipher, including triple DES and AES. The modes are summarized in Table 20.4 .