University of Virginia, Department of Computer Science CS588: Cryptography, Spring 2005

### Quiz

22 March 2005

Name:   Colleen M. Hacker

Work alone. No notes. No books. No other materials. Answer all questions (both sides).

RSA Paper
1. Here is the RSA algorithm, with some pieces missing. Fill in the blanks:

1. Pick 2 large secret primes, p and q.

2. Let n = pq

3. Choose e and d so: ed ≡ 1 mod (p - 1)(q - 1) or φ(n)
4. Encryption function (public): E(M) = Me mod n.

5. Decryption function (private): D(C) = Cd mod n

2. What is the private key?

d
(Note that p and q must be kept secret, but they are not part of the private key. They should be destroyed after e and d are choosen.)

3. What is the range of M that can be reliably transmitted using RSA?

0 ≤ M < n
Since the exponentiation is done mod n the value of M must be less than n.

4. What is φ(185)? (Hint: divide by 5)

185 = 5 * 37
For all primes p, φ(p) = p - 1.
So, φ(185) = φ(37) * φ(5) = 36 * 4 = 144.

Practical Techniques for Searches on Encrypted Data

5. Check all of the below statements that are true about the paper:
1. ___ It describes techniques for searching encrypted data that can search a document of length n in O(n2) stream cipher and block cipher operations.
2. ___ It describes techniques for searching encrypted data that can search a document of length n in O(n) stream cipher and block cipher operations.
3. ___ It mentions the birthday paradox.
4. ___ It presents techniques that are provably secure.
5. ___ For the final scheme, when Alice sends a search query to Bob, Bob can learn something about which documents contain Alice's query term.
All of the statements are true. Some people were tricked by (a). Recall that O establishes an upper bound. If an algorithm is O(n), it also must be O (n2) or any function that grows faster than n. All of the other statements follow directly from the paper.
Security of RSA