Practice exam 2 - Set 2

Multiple-choice test

1. (1 pt) The number of points on an elliptic curve secure from the point of view of cryptographic applications

a. has to be prime
b. has to be equal to the order of the underlying field GF(q)
c. has to be odd
d. has to have a large prime factor

2. (1 pt) The improvement in the ratio of the message size to the ciphertext size obtained by applying the Elliptic Curve Menezes-Vanstone cryptosystem instead of the Elliptic Curve El-Gamal Encryption scheme is equal to
  1. 3/2
  2. 4/3
  3. 2
  4. 3

Describe your assumptions, if any.


3. (1 pt) The number of possible dimensions (formats) of smart cards approved by the ISO standards is equal to

  1. 1
  2. 2
  3. 3
  4. 4

4. (1 pt) Assuming that a seed in a pseudorandom generator used in BSAFE 3.x is created using the current date and time, the most efficient attack against this generator is
  1. exhaustive state search
  2. back tracking
  3. cycle shortening
  4. timing attack
  5. seeding search

5. (1 pt) As a countermeasure against timing cryptanalysis the signature of message M is computed according to the following formula SGN(M) = (((M× V)d mod N) × W) mod N. Determine which of the following values of V and W give the correct value of the signature SGN(M) (list all correct answers):

a. V=R, W=(R-1)d mod N , R random number

b. V=((R-1)d) mod N, W=R, R random number

c. V=R2, W=((R-1)2d) mod N, R random number

d. V=((R-1)e) mod N, W=R, R random number

6. (1 pt) Assuming a four-level hierarchy of the certification authorities (central-state-city-institution) and the fact that each user receives a public key of the central certification authority during his/her registration, how many signature verification operations need to be performed by a student from GMU verifying a message signed by a student from MIT (assume that all CRLs have been verified earlier).

  1. 3
  2. 4
  3. 5
  4. 6

 
Short problems

  1. (3 pts) Check whether there exist a point of the elliptic curve y2 = x3 + 4x + 1 over GF(11) with the x-coordinate equal to 5. If so, please, compute the value of the y-coordinate of this point.
    2.  
  2. (3 pts) In the Shamir's (3, 4) threshold scheme over GF(13), shares of users no. 1, 3, and 4 are equal to 0, 2, and 9, respectively. Find the share of user no. 2.
    3.  
  3. (3 pts) Find a value of the autocorrelation function A(4) for the pseudo-random sequence that consists of the first 34 bits generated by the LFSR <4, 1 + D3 + D4> initialized to [0, 1, 1, 1]. Determine if this sequence passes the autocorrelation test.