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CMSC 414 F06 Exam 1 Page 1 of 8 Name:_________________________
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Total points: 40. Total time: 75 minutes. 6 problems over 6 pages. No book, notes, or calculator
1. [14 points]
Are n=187 and e=9 valid numbers for RSA. Explain. If you answer yes, obtain the corresponding d.
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Solution
There are two requirements:
n must be a product of two primes
e must be relatively prime to f(n) (so that d, which equals e-1 mod-n, exists)
First requirement [2 points]
n = 187 = 11·17. 11 and 17 are primes. So this holds.
Second requirement [6 points]
Recall that if n =p·q where p and q are distinct primes, then f(p q) = (p-1) (q-1)
So f(187) = (11-1) (17-1) = 160.
e, which equals 9, is relatively prime to 160 (because 9=32 and 160=10·16=2·5·24=25·5)
So this requirement holds.
Obtaining d ...

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