# Past Exam for CMSC 414 - CMPTR & NETWORK SECURITY at Maryland (UMD)

## Exam Information

 Material Type: Exam 1 Professor: Staff Class: CMSC 414 - CMPTR & NETWORK SECURITY Subject: Computer Science University: University of Maryland Term: -- Keywords: ParticularlyExplanationAuthenticationConjunctionThe MessageDestinationTotal NumberInfrastructureInitializationRelatively Prime

## Sample Document Text

CMSC 414 F07 Exam 1 SOLUTION Page 1 of 11 Name:___________________ _____________________________________________________________________________________ Total points: 60. Total time: 75 minutes. 6 problems over 7 pages. No book, notes, or calculator 1. [14 points] Are n=323 and e=5 valid numbers for RSA. Explain. If you answer yes, obtain the corresponding d. _____________________________________________________________________ Solution There are two requirements: square4 n must be a product of two primes square4 e must be relatively prime to ?(n) (so that d, which equals e?1 mod-n, exists) First requirement [2 points] n = 323 = 17·19. 17 and 19 are primes. So this holds. Second requirement [4 points] Recall that if n =p·q where p and q are distinct primes, then ?(p?q) = (p?1)?(q?1) So ?(323) = (17?1)?(19?1) = 288. e, which equals 5, is relatively prime to 288 (because 5 is prime and does not divide 288 exactly) So this requir...

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