Cochin University of Science and Techology (CUST) 2008 M.C.A Computer Aplications NUMBER THEORY AND CRYPTOGRAPHY - Question Paper

MCA DEGREE II SEMESTER EXAMINATION, APRIL 2008

CAS 2202 NUMBER THEORY AND CRYPTOGRAPHY

Time: 3 Hours    Maximum marks : SO

PART A

<    (Answer ALL questions)

(AH questions carry EQUAL marks)

(15x2-30)

I.    a. State the Euclidean algorithm and its extension.

b.    Show that the number of primes is infinite.

c.    Find the number of divisors of 9504.

II.    a. Find the least positive incongruent solutions of 36x 27(mod 45).

b.    If p is prime, then show that 2(/>-3)f+l is a multiple of p.

c.    Evaluate the Legendre symbol (221/399).

III.    a. Whai do you mean by cryptanalysis? Why is cryptanalysis important?

b.    Differentiate between confusion and diffusion as applied to cryptosystems.

c.    Discuss the 4 important aspects of mfoimatiofl security.

IV.    a. Compare the security aspects of RSA and ECC cryptosystems.

b.    Write the Diffie-Hellman protocol for key exchange.

c.    What are the schemes for commercial key distribution in symmetric and public key cryptography?

V.    a. Write the desirable properties of hash functions.

b.    Compare the features of MD5 and SHA-1.

c.    What are the features of Kerberos?

PART B

(All questions carry EQUAL marks)

(5x4 = 20)

VI.    A. Using the fundamental principles, show that if csi(modm) and cd(modn), then (i)

or + cy * bx + rfy(mod m) (ii) ac 6</(mod m) and (iii) a' 6* (mod m), where a_tb_tc,d, m,/i c Z*.

OR

B. State and prove the Eulers theorem. Deduce the Fermats little theorem from Eulers theorem.

VII.    A. Solve x*l(mod3), jcz2(mod4), x*3(raod7) and jrs4(modll).

OR

B. Show that tf gcd(a,m) = g and g / b, then the congruence ax (modm) has exactly g incongruent solutions, where a,b,g,m Z.

(Turn over)

(2)

Discuss die different modes of block cipher operation. Which mode is the best? Justify your answer.

OR

Analyse the strength of DES using parameters such as SAC, BIC. confusion, diffusion, etc. Discuss the after effects of DES challenges.

Prove the RSA algorithm.

OR

How are key exchange and encryption/decryption done in elliptic curve cryptography?

Write the digital signature algorithm describing the key generation, signature generation and verification.

OR

Write the SHA-1 algorithm.

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Earning:   Approval pending.