A Course in Mathematical Cryptography by Gilbert Baumslag

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 e-book is worried with the mathematical, specifically algebraic, elements of cryptography. It grew out of many classes awarded by means of the authors over the last 20 years at quite a few universities and covers quite a lot of themes in mathematical cryptography. it really is essentially geared in the direction of graduate scholars and complex undergraduates in arithmetic and computing device technological know-how, 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 several other distinctive issues such as

- Group-Based Cryptography
- Gröbner foundation equipment in Cryptography
- Lattice-Based Cryptography

Show description

Read Online or Download A Course in Mathematical Cryptography PDF

Best cryptography books

Hieroglyphs: A Very Short Introduction (Very Short Introductions)

Hieroglyphs have been way over a language. They have been an omnipresent and omnipotent strength in speaking the messages of historic Egyptian tradition for over 3 thousand years. This old type of expression used to be used as paintings, as a way of selecting Egyptian-ness, even for conversation with the gods.

Understanding Windows CardSpace : an introduction to the concepts and challenges of digital identities

Wi>Understanding home windows CardSpaceis the 1st insider’s consultant to home windows CardSpace and the wider subject of id administration for technical and enterprise execs. Drawing at the authors’ unprecedented adventure earned through operating with the CardSpace product workforce and by way of enforcing cutting-edge CardSpace-based structures at top businesses, it deals unheard of perception into the realities of id administration: from making plans and layout via deployment.

Pairing-Based Cryptography – Pairing 2012: 5th International Conference, Cologne, Germany, May 16-18, 2012, Revised Selected Papers

This ebook constitutes the refereed court cases of the fifth overseas convention on Pairing-Based Cryptography, Pairing 2012, held in Cologne, Germany, in might 2012. The 17 complete papers for presentation on the educational song and three complete papers for presentation on the business song have been conscientiously reviewed and chosen from forty nine submissions.

Cryptography Extensions Practical Guide for Programmers

For a very long time, there was a necessity for a realistic, down-to-earth builders e-book for the Java Cryptography Extension. i'm more than happy to work out there's now a booklet which can solution a few of the technical questions that builders, managers, and researchers have approximately this kind of serious subject. i'm definite that this e-book will give a contribution enormously to the luck of securing Java functions and deployments for e-business.

Additional info for A Course in Mathematical Cryptography

Sample text

Recall that a block cipher encrypts n-letter blocks by n-letter blocks. Hence if A is the plaintext alphabet then a block cipher is a map f : An → An . Show that a block cipher must be a permutation of An . 5 Given a 4-bit LFSR with feedback function R(a0 , a1 , a2 , a3 ) = c4 a0 + c3 a1 + c2 a2 + c1 a3 ∈ ℤ2 . 6 Starting with (1, 0, 0, 0), we get the output string (0, 0, 0, 1, 1, 1, 1, 0). Calculate the values of c1 , c2 , c3 , c4 that break this LFSR. Let A = {0, 1}, n = 4 and π is a permutation on {1, 2, 3, 4}.

6 Is every encryption map with a finite set of ciphertexts surjective? If we encrypt using a shift cipher explain why discovering one encrypted letter will break the system? All integers can be expressed in binary form, that is only using digits of 0, 1. Explain why in a number theoretic cipher it is only really necessary to encrypt a bit, that is, encrypt a 0 or a 1? 5. If we have a message 20 letters long, what is the probability of randomly guessing the plaintext? ) Encrypt the message NO MORE WAR using an affine cipher with single letter keys a = 7, b = 5.

5: if the encryption map is known, it is infeasible to find the inverse. In most public key cryptosystems the encryption key is made public while the decryption key is secret and known only to the party receiving the communication. Notice that the key space must be fairly extensive to prevent a potential attacker from simply doing an exhaustive search to find the decryption key. Before we discuss specific cryptosystems, we introduce general cryptographic protocols. 7 Cryptographic Protocols Besides secure confidential message transmission there are many other tasks that are important in cryptography, both public key and symmetric key.

Download PDF sample

Rated 4.43 of 5 – based on 12 votes