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CMSC 414 S06 Exam 1 Page 1 of 4 Name:_________________________
_____________________________________________________________________________________
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.
CMSC 414 S06 Exam 1 Page 2 of 4 Name:_________________________
2. [5 points]
Assume that Bob uses RSA and the following hold:
square4 n=15
square4 Bob's signature of message m=2 is 5
square4 Bob's signature of message m=3 is 4
Obtain Bob's signature for the message m=12. Show your derivation here.
3. [5 points]
How many numbers between 1 and 250000 are relatively prime to 250000? Explain
CMSC 414 S06 Exam 1 Page 3 of 4 Name:_________________________
4. [10 points]
Using the efficient algorithm...

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