Cryptanalysis of Number Theoretic Ciphers
At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols.
First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it.
Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.
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Terminology of Cryptography
Divisibility and Arithmetic
Eulers Theorem and Its Consequences
Second Degree Congruences
Random Number Generation
Private Key Ciphers
Public Key Ciphers
Key Exchange Algorithms
Alice and Bob Alice's arithmetic attack bank bit operations Bob's byte Chapter Chinese remainder theorem chooses a random ciphertext coefficients coin compute congruence classes congruence x2 Cryptanalysis Cryptanalysis of Number cryptographic deciphering decryption defined discrete logarithm problem divides eavesdropper element elliptic curve enciphered encryption entropy equation Euler pseudoprime example exclusive-or exponent factoring algorithm fast exponentiation Fermat's little theorem function gcd(a inverse irreducible Jacobi symbol large prime Legendre symbol Lemma linear loop method mod q multiplication number field Number Theoretic Ciphers odd prime OxB7 pairs plaintext polynomial positive integer primality test prime divisor prime number primitive root modulo private key probable prime PROOF protocol prove pseudoprime to base public key quadratic nonresidue quadratic residue quadratic residue modulo random number relatively prime Rijndael secret key sends sieve signature signed solution square roots Step stream cipher strong pseudoprime Suppose trial division