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 QNt 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. (oh i>). Prove that there are integers i andj such that a* - by = dr (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 rr 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 ecurityr ' L L7 marks)
(c) What is DSS ? Explain. (G marks)
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