# 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 2006 Keywords: ParticularlyRequirementRelatively PrimeEnvironmentThe EnvironmentThe MessageAuthenticationThe Internet

## Sample Document Text

CMSC 414 S06 Exam 1 SOL-KEY Page 1 of 4 Name:_________________________ SOLUTION AND GRADING KEY _____________________________________________________________________________________ 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. _____________________________________________________________________ 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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