Introduction to Cryptography
Cryptography is the key technology in electronic key systems, used to keep data secret, digitally sign documents, permit access control, etc. Therefore, users should know not only how its techniques work, but should also be able to estimate their efficiency and security. This accessible book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge, who are interested in modern cryptographic algorithms and their mathematical foundation.
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Congruences and Residue Class Rings
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affine linear Alice chooses Alice's attack baby-step giant-step bigint binary expansion binary length block cipher block length Bob's called Chinese remainder theorem ciphertext coefficients collision resistant compression function congruence Corollary cryptography cryptosystem cyclic group decryption denoted describe determine Diffie-Hellman divides document ECB mode efficient ElGamal signature elliptic curve encryption function Example Exercise exponent exponentiation extended euclidean algorithm factor base factoring algorithms Feistel cipher gcd(a greatest common divisor group element group of residues hash function hash value Hence implies index calculus algorithm inverse key space mod q modp modulo nonnegative obtain Oscar password polynomial positive integer Pr(A prime divisor prime factors prime number private key probability Proof protocol prove public key public-key system quadratic sieve random number real number residue class residue class ring residue classes mod secret key Section semigroup sequence smart card solution solve square roots subgroup verify Z/mZ Z/pZ zero