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Cargando... The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryptionpor Joshua Holden
   Ninguno Actualmente no hay Conversaciones sobre este libro.  themulhern | Aug 5, 2020 |  sin reseñas | añadir una reseña
"The Mathematics of Secrets takes readers on a tour of the mathematics behind cryptography--the science of sending secret messages. Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers operate, as he focuses on both code making and code breaking. He discusses the majority of ancient and modern ciphers currently known, beginning by looking at substitution ciphers, built by substituting one letter or block of letters for another. Explaining one of the simplest and historically well-known ciphers, the Caesar cipher, Holden establishes the key mathematical idea behind the cipher and discusses how to introduce flexibility and additional notation. He explores polyalphabetic substitution ciphers, transposition ciphers, including one developed by the Spartans, connections between ciphers and computer encryption, stream ciphers, ciphers involving exponentiation, and public-key ciphers, where the methods used to encrypt messages are public knowledge, and yet, intended recipients are still the only ones who are able to read the message. Only basic mathematics up to high school algebra is needed to understand and enjoy the book." -- adapted from jacket flap. No se han encontrado descripciones de biblioteca. |
Autor de LibraryThingJoshua Holden es un Autor de LibraryThing, un autor que tiene listada su biblioteca personal en LibraryThing. Debates activosNingunoCubiertas populares
 Google Books — Cargando...GénerosSistema Decimal Melvil (DDC)005.8Information Computer Science; Knowledge and Systems Computer programming, programs, data, security Computer SecurityClasificación de la Biblioteca del CongresoValoraciónPromedio: (5)
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1
It's not a textbook, but it is a great deal more rigorous than your usual popular math book. It's a difficult middle ground and it sometimes fails to deliver.
I really only read the elementary stuff, about the Caesar cypher and affine cyphers. The basic idea is that there is an algorithm which is a simple formula, as:
P = C = K = {0, ..., N}.
p in P, p is a code for a plaintext character
c in C, c is a code for a encrypted character
k in K, k is the encryption key
the generalization of the Caesar cypher yields the following algorithm:
(I) c = p + k mod N + 1
Note that this is a surjective mapping for any k in K. To decrypt:
p = c + (N + 1 - k) mod N + 1. So, N + 1 - k is the additive inverse of k in this modular arithmetic. Note that 0 is the identity here.
Using multiplication instead of addition and changing things slightly:
P = C = {1, ..., N}.
(II) c = p * m mod N
GCD(m, N) = 1.
Example: N = 25, m = 3; N = 8, m = 3
The inverse of m under this relation can be discovered by noticing that if the GCD is 1, then writing out each equation that is yielded by executing the GCD algorithm will yield a series of equation, which with substitution, will give an equation with the form 1 = x * m + y * N. x is the inverse.
Example:
a) 8 = 2 * 3 + 2
b) 3 = 2 * 1 + 1
c) 2 = 1 * 2 + 0
(c) isn't interesting, but (b) and (a) can be rearranged like this:
b') 1 = 3 - 2 * 1
a') 2 = 8 - 2 * 3
Substituting into b':
1 = 3 - (8 - 2 *3) * 1
gathering up the 8's and 3's:
1 = 3 - (8 - 2 * 3)
1 = 3 * 3 - 8
so we can conclude that 3 inverse is 3 here.