Midterm Exam 2 Multiple Choice Test - 2004 | ECE 646, Exams of Cryptography and System Security

Material Type: Exam; Class: Cryptography/Comp Netwk Sec; Subject: Electrical & Computer Enginrg; University: George Mason University; Term: Fall 2004;

Typology: Exams

2019/2020

Uploaded on 11/25/2020

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ECE 646 – Fall 2004
Midterm Exam 2
December 4-5, 2004
Multiple-choice test
1. (0.5 pt) 1024-bit RSA can be securely used in the following block cipher
modes (choose as many as appropriate):
A. CBC
B. counter mode with j=64
C. CFB with j=1024
D. ECB
E. OFB with j=8
2. (0.5 pt) Assuming the use of classical algorithms for exponentiation,
multiplication, and modulo reduction, changing the length of the modulus
N from 512 bits to 2048 bits increases the time taken in software by the
RSA signature generation using Chinese Remainder Theorem by a factor
of:
A. 4
B. 8
C. 16
D. 32
E. 64
F. other
3. (0.5 pt) The number of the RSA messages not concealed by the RSA with
the public key equal to e=3, N=257*421 is equal to:
A. 9
B. 771
C. 1285
D. 216+1
E. 257*421
F. other
pf3
pf4

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ECE 646 – Fall 2004 Midterm Exam 2 December 4-5, 2004

Multiple-choice test

  1. (0.5 pt) 1024-bit RSA can be securely used in the following block cipher modes (choose as many as appropriate):

A. CBC B. counter mode with j= C. CFB with j= D. ECB E. OFB with j=

  1. (0.5 pt) Assuming the use of classical algorithms for exponentiation, multiplication, and modulo reduction, changing the length of the modulus N from 512 bits to 2048 bits increases the time taken in software by the RSA signature generation using Chinese Remainder Theorem by a factor of:

A. 4 B. 8 C. 16 D. 32 E. 64 F. other

  1. (0.5 pt) The number of the RSA messages not concealed by the RSA with the public key equal to e=3, N=257*421 is equal to:

A. 9 B. 771 C. 1285 D. 216 + E. 257* F. other

  1. (0.5 pt) The ratio of the amount of numbers that need to be tested using the Miller-Rabin test to find a prime of the size 1024 bits to the amount of numbers that need to be tested using the Miller-Rabin test to find a prime of the size 256 bits is approximately equal to

A. 2 B. 4 C. 8 D. 16 E. ln 1024 / ln 512 F. other

  1. (0.5 pt) The number of bases a (1 ≤ a ≤ n) for which the Fermat's probabilistic primality test returns the result 'probably prime' for the Carmichael number n = 561 = 3 ⋅ 11 ⋅ 17 is

A. 1

B. 241

C. 320

D. 560

E. 561

F. other

  1. (0.5 pt) The ratio of times necessary to generate the Diffie-Hellman public-private key pair on a smart card without an arithmetic coprocessor for the following two sizes of the system paramater q : k=2048 and k=1024 is

A. 2 B. 4 C. 8 D. 16 E. 32 F. other

  1. (0.5 pt) Assuming a three-level hierarchy of the certification authorities (central-state-institution) and the fact that each user receives a public key of the central certification authority during his/her registration, how many operations involving a private key of the receiver need to be performed

Short problems

  1. (2 pt) Find a private key corresponding to the following RSA public key {e=17, N=19*31}. Sign a message M=2 using the Chinese Remainder Theorem. Show the results of all intermediate modular multiplications. Hints: You can use spreadsheet, such as Excel to perform and document your computations.
  2. (2 pt) Put the following transformations in order according to their execution time in software (start from the transformation which takes the smallest amount of time). Justify your answer by deriving the necessary formulas. Formulate all necessary assumptions.

A. RSA public-private key generation with the modulus N length 1024 bits. B. RSA signature generation using CRT with the 1024-bit d , 512-bit p , and 512-bit q. C. RSA signature verification with e =F 4 =2^16 +1, and the modulus N length 1024 bits. D. RSA decryption using CRT with the 1024-bit d, 256-bit p, and 768-bit q. E. Diffie-Hellman public-private key generation with the modulus p length 1024 bits. F. Diffie-Hellman common secret derivation with the modulus p length 1024 bits.

  1. (2 pt) Demonstrate using the Miller Rabin test with the sufficient number and appropriate values of bases that 59 is a prime with a zero probability of error, and 57 is a composite number. Show the results of all intermediate modular multiplications. Determine the total number of modular multiplications required. Hints: You can use spreadsheet, such as Excel to perform and document your computations. Do not rely on lectures notes only, read carefully Section 4.2.3 from Handbook of Applied Cryptography.