Calicut University 2006 M.C.A , - 2K 201 - NUMBER THEORY AND CRYPTOGRAPHY (New Scheme) - Question Paper

M.C.A Degree Examination, August 2006
MCA 2K 201 - NUMBER THEORY AND CRYPTOGRAPHY (New Scheme)

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SECOND SEMESTER M.OA, DEGREE EXAMINATI QN_t AUGUST 20045

MCA 2K 201NUMBER THEORY AND CRYPTOGRAPHY

{New Scheme)

Time : Three Hours    Maximum : 100 Marks

,4n?ujer nr.y five ifUxi-iions.

All qvesti&nE tarry marts.

1, (a) Define the G,C,H, (Greatest Common Divisor) of two positive numbers-    (2 marks)

(b) Let d - G.C.D. (o_h i>). Prove that there are integers i andj such that a* - by = d_r (7 marks)

(e) Using Extended Euclidean Algorithm, find integers* and v fiuih that 73.t -i- 31v - 1.

   (4 marVs}

(d)    Define prime numbers. _j    _    marks)

(e)    Cheek whether or not the fiuler function is multiplicative.    (5 marks)

Z. (a)    State and prove Fermat's little theorem. Li the converse true ? Why or wby not ?    (8 marks)

(b)    Solve the congruence 2* + 7y s 5 tmod IS). '    marks)

(t)    Solve the Dioph&niine equation x³ + y¹ - i², with 0 < z < 30.    (4 marks)

(d)    State and prove ft'iisons theorem. Is the convene tmft 7 Pmva your assertion.    (6 marks)

3.    (a) State Chinese Hcmainder Theorem- What Ls its relevance 1    (4 marks.}'

(b)    Solve the congruence jc² e iae (mod 401), given that 401 is prime, with 3 as a non-residue

(6 marks}

(c)    Find all those odd primes for whkh 3 is a Quadratic residues.    (6 marks)

(d)    Briefly discuss Block Cipher Principles.    ^r    (4 marks)

4.    (a) What is steganography ? Explain,    (5 marks)

fb) Explain briefly classical encryption techniques,    .    (5 marks}

(c) What do you mean by double encryption is equivalent to single encryption 7 Is this true in the caseoTDES?    .    '

(10 marks)

5.    (a) Briefly explain Block cipher principles. '    [4 marksj

(b)    Explain International Data Encryption Algorithm.    (10 marks)

(c)    Describe BLOWF1SH encryption.    6 marks)

6.    (a) Describe in detail, the USA Algorithm. '    (6 marks)

<b) A point P on the elliptic curve is said to be of order r_r ifr is the smallest + ve integer such that rP = 0. Prove that the order of the point P = (> 3) on y¹ h i³ + 1 is 6.

[6 marks)

fo) Explain the role of Hash function in cryptography    (3 marks)

7.    (a) Explain SHA-1 algorithm.    tB marks)

(b)    Write short ,iote on multimedia 5 ecurity_r    ' ^L    L7 marks)

(c)    What is DSS ? Explain.    (G marks)

Attachment: calicut-university-2006-m-c-a--32584-1.pdf

Earning:   Approval pending.