By Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman

This self-contained creation to fashionable cryptography emphasizes the math in the back of the idea of public key cryptosystems and electronic signature schemes. The e-book makes a speciality of those key subject matters whereas constructing the mathematical instruments wanted for the development and safeguard research of various cryptosystems. basically uncomplicated linear algebra is needed of the reader; options from algebra, quantity concept, and likelihood are brought and constructed as required. this article presents an awesome creation for arithmetic and laptop technological know-how scholars to the mathematical foundations of contemporary cryptography. The ebook comprises an intensive bibliography and index; supplementary fabrics can be found online.

The booklet covers quite a few subject matters which are thought of significant to mathematical cryptography. Key themes include:

  • classical cryptographic buildings, equivalent to DiffieHellmann key trade, discrete logarithm-based cryptosystems, the RSA cryptosystem, and electronic signatures;
  • fundamental mathematical instruments for cryptography, together with primality checking out, factorization algorithms, chance idea, details idea, and collision algorithms;
  • an in-depth remedy of significant cryptographic techniques, akin to elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.

The moment variation of An creation to Mathematical Cryptography features a major revision of the cloth on electronic signatures, together with an previous advent to RSA, Elgamal, and DSA signatures, and new fabric on lattice-based signatures and rejection sampling. Many sections were rewritten or increased for readability, specifically within the chapters on info concept, elliptic curves, and lattices, and the bankruptcy of extra subject matters has been improved to incorporate sections on electronic money and homomorphic encryption. quite a few new workouts were included.

Show description

Read Online or Download An Introduction to Mathematical Cryptography PDF

Best information theory books

Quantentheorie der Information: Zur Naturphilosophie der Theorie der Ur-Alternativen und einer abstrakten Theorie der Information

NEUER textual content! !! Holger Lyre unternimmt den grenzüberschreitenden Versuch, sowohl in die philosophisch-begrifflichen als auch physikalisch-mathematischen Zusammenhänge von Informations- und Quantentheorie einzudringen. Ausgehend von Carl Friedrich von Weizsäckers "Quantentheorie der Ur-Alternativen" wird eine abstrakte Theorie der info in transzendentalphilosophischer Perspektive entworfen und werden die begrifflichen Implikationen einer konsequenten Quantentheorie der details umfassend diskutiert.

Probability, Random Processes, and Ergodic Properties

Likelihood, Random procedures, and Ergodic houses is for mathematically susceptible information/communication theorists and other people operating in sign processing. it is going to additionally curiosity these operating with random or stochastic methods, together with mathematicians, statisticians, and economists. Highlights: whole journey of e-book and instructions to be used given in creation, so readers can see at a look the themes of curiosity.

Extra resources for An Introduction to Mathematical Cryptography

Example text

For example, if Alice and Bob use a simple substitution cipher, they should assume that Eve is aware of this fact. This illustrates a basic premise of modern cryptography called Kerckhoff ’s principle, which says that the security of a cryptosystem should depend only on the secrecy of the key, and not on the secrecy of the encryption algorithm itself. If (K, M, C, e, d) is to be a successful cipher, it must have the following properties: 1. For any key k ∈ K and plaintext m ∈ M, it must be easy to compute the ciphertext ek (m).

Powers and Primitive Roots in Finite Fields 31 If p | a, then it is clear that every power of a is divisible by p. So we only need to consider the case that p a. , (p − 1)a reduced modulo p. 8) There are p − 1 numbers in this list, and we claim that they are all different. To see why, take any two of them, say ja mod p and ka mod p, and suppose that they are the same. This means that ja ≡ ka (mod p), (j − k)a ≡ 0 and hence that (mod p). Thus p divides the product (j − k)a. 19 tells us that either p divides j − k or p divides a.

3. 1 Modular Arithmetic and Shift Ciphers Recall that the Caesar (or shift) cipher studied in Sect. 1 works by shifting each letter in the alphabet a fixed number of letters. 7. 7: Assigning numbers to letters Then a shift cipher with shift k takes a plaintext letter corresponding to the number p and assigns it to the ciphertext letter corresponding to the number p + k mod 26. Notice how the use of modular arithmetic, in this case modulo 26, simplifies the description of the shift cipher. The shift amount serves as both the encryption key and the decryption key.

Download PDF sample

Rated 4.36 of 5 – based on 49 votes