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 booklet is anxious with the mathematical, specifically algebraic, elements of cryptography. It grew out of many classes offered through the authors during the last 20 years at a number of universities and covers quite a lot of subject matters in mathematical cryptography. it truly is essentially geared in the direction of graduate scholars and complicated undergraduates in arithmetic and machine technology, yet can also be of curiosity to researchers within the area.
Besides the classical tools of symmetric and personal key encryption, the booklet treats the math of cryptographic protocols and several other specific issues such as
- Group-Based Cryptography
- Gröbner foundation equipment in Cryptography
- Lattice-Based Cryptography
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Extra info for A Course in Mathematical Cryptography
For each si there is an encryption map fsi and a corresponding decryption map gei . Let F denote the overall encryption map. Then we would have F(a1 a2 ⋅ ⋅ ⋅ ak ) = fs1 (a1 )fs2 (a2 ) ⋅ ⋅ ⋅ fsk (ak ). In practice the plaintext characters are usually single bits 0, 1. Stream ciphers typically encrypt and decrypt at higher speeds than block ciphers and can usually be decrypted synchronously with the encryption. Stream ciphers are an attempt to approximate the security of so-called one-time pads.
The communicating parties decide on a keyword. This is private between the communicators. To encrypt the keyword is placed above the plaintext message over and over until each plaintext letter lies below a letter in the keyword. The ciphertext letter corresponding to a given plaintext letter is determined by the alphabet at the intersection of the keyword letter and plaintext letter below it. To clarify this description, and make Vigènere encryption precise, we repeat the example given in Chapter 1.
As before consider A as ℤN and treat them as the modular ring. Consider plaintext messages as elements of ℤN and consider the encryption map f (n) ≡ n2 (mod N). Is this a good encryption map? Why or why not? 1 Mixed Encryption Modern cryptography is usually separated into symmetric key cryptography and public key cryptography. In symmetric key cryptography, both the encryption and decryption keys are supposedly known only to the sender and receiver, usually referred to as Bob and Alice. In public key cryptography, the encryption map is public knowledge but only the receiver knows how to decode.