Download A Course in Mathematical Cryptography by Gilbert Baumslag PDF

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 publication is worried with the mathematical, specifically algebraic, facets of cryptography. It grew out of many classes provided through the authors over the last two decades at numerous universities and covers quite a lot of themes in mathematical cryptography. it truly is essentially geared in the direction of graduate scholars and complicated undergraduates in arithmetic and laptop technology, yet can also be of curiosity to researchers within the area.

Besides the classical equipment of symmetric and personal key encryption, the ebook treats the maths of cryptographic protocols and a number of other distinct issues 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

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2 Block Ciphers | 21 Iterated Block Ciphers The difficulty of creating a secure block cipher which is easy to implement and allows efficient encryption and decryption is usually met by repeatedly applying simple operations such as substitutions and permutations. The resulting ciphers are called iterated block ciphers or product ciphers. An input block of plaintext is subjected to repeated applications of a fixed set of mappings. Each iteration in this scheme is called a round. Each round may use a separate encryption maps and a separate key.

7 Cryptographic Protocols | 15 E = a set of injective maps fk : P → C indexed by the key space. This is called the set of encryption maps. Hence, for each k ∈ K, there is an injective map fk : P → C. D = a set of maps gk???? : C → P also indexed by the key space. This is called the set of decryption maps. The central property of a cryptosystem is that, for each k ∈ K, there exists a corresponding key k???? ∈ K and a decryption map gk???? : C → P such that gk???? is the left inverse of fk . In other words, for every plaintext message unit m, we have gk???? (fk (m)) = m.

Further at each round, the round key is combined with some group operation such as XOR. The operation XOR is simply addition modulo 2 on the bits {0, 1}. Decryption is done by simply reversing the encryption process. Here the inverses of the S-boxes and permutations are applied by using the round keys in reverse order. The ideas used in a substitution-permutation network become important when we discuss the modern standard block cipher protocol AES. Another important type of iterated block cipher is a Feistel network.

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