## Exam Information

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CMSC 414 S06 Exam 1 SOL-KEY Page 1 of 4 Name:_________________________
SOLUTION AND GRADING KEY
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Total points: 30. Total time: 115 minutes. 4 problems over 4 pages. No book, notes, or calculator
1. [10 points]
Suppose Bob uses RSA with n=77 and e=5.
Are these valid numbers for RSA. Explain.
If you answer yes, obtain the corresponding d.
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There are two requirements:
square4 n must be a product of two primes [1 point]
square4 e must be relatively prime to ?(n) (so that d, which equals e?1 mod-n, exists) [1 point]
First requirement [2 points]
n = 77 = 7?11. 7 and 11 are primes. So this holds.
Second requirement [6 points]
Recall that if n = p1a1 ? p2a2 ? ? ? pkak where pi is prime, then
?( p1a1 ? p2a2 ? ? ? pkak ) = (p1?1)?p1a1?1 ? (p2?1)?p2a2?1 ??? (pk?1)?pkak?1
So ?(77) = (7?1)?(11?1) = 60.
e...

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