By Philip N. Klein
Cryptography has been hired in struggle and international relations from the time of Julius Caesar. In our web age, cryptography's such a lot common software should be for trade, from retaining the safety of digital transfers to guarding conversation from commercial espionage. This available creation for undergraduates explains the cryptographic protocols for attaining privateness of communique and using electronic signatures for certifying the validity, integrity, and starting place of a message, record, or software. instead of delivering a how-to on configuring net browsers and electronic mail courses, the writer presents a consultant to the rules and trouble-free arithmetic underlying smooth cryptography, giving readers a glance lower than the hood for protection suggestions and the explanations they're considered safe.
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Extra resources for A Cryptography Primer: Secrets and Promises
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. We define b rem m to denote the value of r described in the Quotient-and-Remainder Theorem.
The remainder of 51 divided by 7 is 2, so 2 is also the representative of 51. Therefore 30 is congruent to 2 and 51 is congruent to 2, so 30 and 51 are congruent to each other. Showing non-congruence We see that we can use rem to show that two integers are congruent to each other. Can we use rem to show that two integers are not congruent to each other? We use the following argument. Suppose that a and b are congruent (mod m). Because a is congruent to its representative and b is congruent to a, it follows that b is congruent to a’s representative.
Which are onto? • The domain is the set of undergraduates at Brown; the rule is x → x’s ID number 42 4 Functions • The domain is the set of undergraduates at Brown; the rule is x → number of hairs on x’s head • The domain is the set of staff at Brown; the rule is x → x’s salary • The domain is the set of all living people; the rule is x → x’s mother • The domain is the set of all commercial stereos; the rule is x → x’s manufacturer Of course, one can easily specify a domain and a rule for something that is not really a function.
A Cryptography Primer: Secrets and Promises by Philip N. Klein