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

## Exam Information

 Material Type: Exam 1 Professor: Shankar Class: CMSC 414 - CMPTR & NETWORK SECURITY Subject: Computer Science University: University of Maryland Term: Spring 2009 Keywords: ParticularlyAuthenticationExplanationOrganizationEnvironmentThe InternetThe MessageInitializationInfrastructureDestination

## Sample Document Text

CMSC 414 S09 Exam 1 Page 1 of 6 Name:____________________________________ ____________________________________________________________________________________________________ Total points: 55. Total time: 75 minutes. 6 problems over 6 pages. No book, notes, or calculator 1. [10 points] Are n=221 and d=35 valid numbers for RSA. Explain. If you answer yes, obtain the corresponding e. _____________________________________________________________________ Solution There are two requirements: . n must be a product of two primes . e must be relatively prime to ?(n) (so that d, which equals e?1 mod-n, exists) First requirement [2 points] n = 221 = 13·17. 13 and 17 are primes. So this holds. Second requirement [2 points] If n =p·q where p and q are distinct primes, then ?(p?q) = (p?1)?(q?1) So ?(221) = (13?1)?(17?1) = 12·16 = 192 gcd(35, 192) = 1 [because 35 = 7·5 and 192 = 26.3, so they have no factors in common] So e=35 is valid. ...

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