By Philip N. Klein
Cryptography has been hired in battle and international relations from the time of Julius Caesar. In our web age, cryptography's so much frequent program should be for trade, from maintaining the safety of digital transfers to guarding conversation from business espionage. This available advent for undergraduates explains the cryptographic protocols for reaching privateness of communique and using electronic signatures for certifying the validity, integrity, and foundation of a message, rfile, or application. instead of delivering a how-to on configuring internet browsers and email 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 defense options and the explanations they're considered safe.
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Extra resources for A Cryptography Primer: Secrets and Promises
1 (ECB stands for “Electronic Code Book”). 1. A diagram illustrating ECB mode. breaks her plaintext into blocks. The first block consists of the first 12 digits, the second block consists of the next 12 digits, and so on. There are five such blocks in this case; the last block has some extra zeroes to “pad” it out to the right length. Next, Alice encrypts each block separately. The same key is used for all the blocks. Finally, she takes her cyphertext to be the sequence of encryptions of the blocks.
Now 102 is 10 · 10. Because 10 is congruent to 1, 10 · 10 is congruent to 1 · 1, which is 1, so 8 · 102 is congruent to 8 · 1, which is 8. • Finally, consider 5 · 103 . By the same reasoning, 103 is congruent to 1, so 5 · 103 is congruent to 5. Putting these statements together, 5 · 103 + 8 · 102 + 3 · 10 + 7 is congruent to 5 + 9 + 3 + 7. That is, the number 5837 is congruent to the sum of its digits. This process applies to any positive number: Because 10, 102, 103 and higher powers of 10 are all congruent to 1 (modulo 9), any positive integer is congruent (modulo 9) to the sum of its digits.
Cyph. ≡ Jan. plain − Feb. plain(mod 1020 ) Because Eve knows the cyphertexts from January and February, she can subtract modulo 1020 to obtain the mod 1020 difference between the January plaintext and the February plaintext. That is, she obtains the mod-1020 representative of the difference between January’s advertising budget and February’s. The true difference is either the mod-1020 representative of the difference (if the true difference is positive) or else it is the mod-1020 representative minus 1020 (if the true difference is negative).
A Cryptography Primer: Secrets and Promises by Philip N. Klein