Download e-book for iPad: A Cryptography Primer: Secrets and Promises by Philip N. Klein

By Philip N. Klein

ISBN-10: 1107017882

ISBN-13: 9781107017887

Cryptography has been hired in warfare and international relations from the time of Julius Caesar. In our web age, cryptography's such a lot frequent software could be for trade, from maintaining the safety of digital transfers to guarding communique from commercial espionage. This available advent for undergraduates explains the cryptographic protocols for reaching privateness of conversation and using electronic signatures for certifying the validity, integrity, and starting place of a message, record, or application. instead of supplying a how-to on configuring internet browsers and e mail courses, the writer presents a advisor to the foundations and straight forward arithmetic underlying glossy cryptography, giving readers a glance less than the hood for defense innovations and the explanations they're regarded as safe.

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Extra info for A Cryptography Primer: Secrets and Promises

Sample text

1012 ). Imagine the Caesar cypher done with an alien alphabet that consists of 1012 letters. The key will be a representative with respect to this modulus, namely any number from 0 to 999999999999. To encrypt a single letter of the alien alphabet, one adds the corresponding number to the key; the result, reduced to a representative (a nonnegative integer less than 1012 ), is one letter of cyphertext. We would like to use this system with plaintexts written in our own puny alphabet. Here is one way to do this: we use a number from 0 to 999999999999 to represent a sequence of six symbols.

1 does not. 1 fails to be a function. There are elements of the first set (namely 1) that maps to two things, and there are elements (namely 6) that map to no elements. The first set is called the domain of the function, and the second set is called the codomain. 2 is the set {0, 1, 2, 3, 4, 5}, and the codomain is {0, 1, 2, 4, 6, 12, 20}. e. has an arrow pointing to it). That is, there are elements of the codomain (namely 2 and 4) that have no incoming arrows. This is fine; it does not violate the definition of a function.

1) Examples: • Let b = 25 and let m = 7 . Then Eq. 1) is satisfied by q = 3 and r = 4. ) • Let b = 62 and let m = 7. Then Eq. 1) is satisfied by q = 8 and r = 4. ) • Let b = 99 and let m = 12. Then Eq. 1) is satisfied by q = 8 and r = 3. ) As the examples suggest, r is the remainder when b is divided by m, and q is the quotient. Finding the remainder is an arithmetic operation just like addition and multiplication. In the spirit of the + and the × operators, therefore, we define a operator, rem, to signify taking the remainder.

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A Cryptography Primer: Secrets and Promises by Philip N. Klein

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