A Course in Number Theory and CryptographySpringer Science & Business Media, 6 dic 2012 - 208 pagine The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. Because number theory and cryptography are fast-moving fields, this new edition contains substantial revisions and updated references. |
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1-to-1 correspondence 26-letter alphabet b₁ base bit operations required Carmichael number Chinese Remainder Theorem choose ciphertext composite compute congruence continued fraction cryptography deciphering key denote digits digraphs discrete log problem divide divisible elements elliptic curve enciphering key enciphering matrix enciphering transformation encryption equation estimate Euclidean algorithm Euler pseudoprime example Exercise Fermat's Little Theorem finite field follows formula Gaussian integers gives inverse irreducible polynomials knapsack problem large prime least nonnegative residue Legendre symbol letters linear monic irreducible polynomials multiple N-letter nonresidue nonzero number of bit number theory numerical equivalents obtain P₁ pair plaintext plaintext message units positive integer primality test prime factors prime number prime power Prove public key cryptosystem quadratic real number residue modulo root of unity solution square root strong pseudoprime suppose vector write Z/nZ zero