By Gilbert Baumslag

The topic of this ebook is mathematical cryptography. by means of this we suggest the math interested by cryptographic protocols. because the box has elevated, utilizing either commutative and noncommutative algebraic items as cryptographic systems, a booklet describing and explaining a majority of these mathematical equipment is of immeasurable worth.

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From this definition, Shannon proved that the one-time pad, that we describe shortly, has perfect security. Perfect security is difficult to obtain. Closely related is semantic security. This is the appropriate notion of security relative to a passive attacker. A cryptosystem is semantically secure relative to given security assumptions if it is infeasible for a pas- 36 | 3 Cryptanalysis and Complexity sive attacker to determine relevant information about a plaintext given an observation of a ciphertext.

Another important type of iterated block cipher is a Feistel network. It became the basis for the first widely accepted encryption standard. 4 we introduce this topic in detail. There are two main methods for cryptanalysis of block ciphers; linear cryptanalysis and differential cryptanalysis. We will discuss these in Chapter 3. Block Cipher Modes of Operation There are several different variations of block ciphers, each addressing certain security problems of the basic design. We will discuss security and secrecy in the next chapter and then delve more deeply into these variations.

Cryptanalysis depends also on a knowledge of the form of the code, that is, the type of encryption algorithm employed. Most classical cryptanalysis depends on a statistical frequency analysis of the ciphertext versus the plaintext. An example of a statistical frequency attack is presented in the next section. First we describe various types of cryptoanalytic attacks. The security of a cryptosystem or general cryptographic protocol depends on its ability to withstand these attacks. In addition, the attack and its chance of success depend upon the security assumptions made.