By Gilbert Baumslag
Cryptography has turn into crucial as financial institution transactions, bank card infor-mation, contracts, and delicate clinical info are despatched via inse-cure channels. This ebook is worried with the mathematical, particularly algebraic, points of cryptography. It grew out of many classes provided by means of the authors during the last two decades at quite a few universities and covers quite a lot of issues in mathematical cryptography. it truly is basically geared in the direction of graduate scholars and complicated undergraduates in arithmetic and computing device technological know-how, yet can also be of curiosity to researchers within the area.
Besides the classical tools of symmetric and personal key encryption, the e-book treats the maths of cryptographic protocols and a number of other precise subject matters such as
- Group-Based Cryptography
- Gröbner foundation tools in Cryptography
- Lattice-Based Cryptography
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Extra resources for A Course in Mathematical Cryptography
An attack usually attempts to take advantage of some weakness in the encryption algorithm that allows one to decode. 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.
The set of algorithms and procedures needed to accomplish a cryptographic task is called a cryptographic protocol. A cryptosystem is just one type of cryptographic protocol. 1. Suppose that several parties want to manage a cryptographical task. Then they must communicate with each and cooperate. Hence each party must follow certain rules and implement certain agreed upon algorithms. The set of all such methods and rules to perform a cryptographical task is called a cryptographic protocol. 16 | 1 Basic Ideas of Cryptography We now list several cryptographic tasks.
This is formally defined in terms of encrypted bits. Let ???? = 0, 1 be an encrypted bit. In the absence of any information, the determination of ???? is entirely random, and hence, the probability of correctly determining ???? is 12 . Given a set of security assumptions, then a cryptosystem is said to be broken, and an attack successful, if by using the attack, the probability of correctly determining an encrypted bit is greater than 12 , within a feasible time frame of the encryption. We make this precise.