Neal Koblitz A Course In Number Theory And Cryptography Pdf 11: A Classic Textbook on Cryptography

The course will study classical and new public key cryptography. Systems, whose hardness is based on factoring, such as RSA; discrete logs in abelian groups , such as the Diffie-Hellman key exchange and El-Gamal with elliptic curves; lattices, such as NTRU and ring learning with errors, will be featured. Featured also will be the standard attacks on these systems.

• Contents Classical systems like Caesar and Vigenère, some simple cryptanalysis.

• The general structure of block ciphers, Feistel ciphers like DES, AES, the most suitable modes-of-use, e.g. CBC or OFB.

• Shift register sequences (linear and non-linear), the linear complexity of a periodic sequence, the Berlekamp-Massey algorithm.

• The principle of public key cryptography.

• Basics of finite fields and their arithmetic.

• Diffie-Hellman key exchange, El Gamal, several methods to take discrete logarithms (baby-step giant-step method, the Pohlig-Hellman method, Pollard-rho and the index calculus method).

• Elliptic curve cryptosystems.

• The RSA system for encryption and signing, generating prime numbers by means of probabilistic primality tests, several factorization algorithms (Pollard-(p-1), Pollard-rho, the random square method, the quadratic sieve method), and some insecure modes of RSA.

• Hash functions, Message Authentication Codes

Neal Koblitz A Course In Number Theory And Cryptography Pdf 11

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Our purpose is to give an overview of the applications of number theory to public-key cryptography. We conclude by describing some tantalizing unsolved problems of number theory that turn out to have a bearing on the security of certain cryptosystems.

08 Dec 2014 Lecture given by Jens Bauch.Concept of public-key cryptography, some recap of number theorybackground (multiplicative group modulo n, Euler-phi function, Euler'stheorem), public key for RSA is (e,n), private key is d, where n=pqfor two different primes p and q, φ(n)=(p-1)(q-1) and d is theinverse of e modulo φ(n); encryption, decryption, sign,verify. Attention, this is schoolbook RSA, do not usethis in practice. For functionality (and security) we want to sign h(m)and not m.Exponentiation by square and multiply and how many operations thistakes, examples; can choose small e but d must be large/random. Firstproblem with schoolbook multiplication: we can recover a message thatis sent to multiple people, if they all use the same small exponent.Jens scanned his class prep for youinstead of pictures. 2ff7e9595c