By Gilbert Baumslag
Cryptography has turn into crucial as financial institution transactions, bank card infor-mation, contracts, and delicate clinical details are despatched via inse-cure channels. This ebook is anxious with the mathematical, specifically algebraic, elements of cryptography. It grew out of many classes offered by means of the authors over the last two decades at a variety of universities and covers a variety of issues in mathematical cryptography. it's basically geared in the direction of graduate scholars and complicated undergraduates in arithmetic and desktop technology, yet can also be of curiosity to researchers within the area.
Besides the classical tools of symmetric and personal key encryption, the publication treats the maths of cryptographic protocols and several other precise issues such as
- Group-Based Cryptography
- Gröbner foundation equipment in Cryptography
- Lattice-Based Cryptography
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Additional resources for A Course in Mathematical Cryptography
In assessing cryptographic security we must also consider whether we have a possible passive attacker or a possible active attacker. A passive attacker can only look at encrypted transmissions but cannot interfere or change them at all. On the other hand, an active attacker has the ability to perhaps modify encrypted transmissions. A very powerful technique along these lines is called the man in the middle attack. Suppose Bob wants to communicate with Alice. The attacker gets in the middle and intercepts Bob’s message.
A decision problem is in non-deterministic polynomial time if a person with unlimited computing power not only can answer the problem but if the answer is “yes” the solver can supply evidence that another person could use to verify the correctness of the answer in polynomial time. The demonstration that the “yes” answer is correct is called a polynomial time certificate. The class of non-deterministic polynomial time problems is denoted by NP. The class co-NP consists of problems like those in NP but with “yes” replaced by “no”.
With this method one can try to determine the length of the key word. If the same partial word appears in the plaintext occurs several times then in general it will be encrypted differently. However, if the distance between the first letter of the respective partial word is a multiple of the key word length then the partial word will be encrypted the same. We have to look for partial sequences of length ≥ 3 in the cipher text. There respective distances are probably divisible by the length of the key word.
A Course in Mathematical Cryptography by Gilbert Baumslag