InterviewSolution

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51.	5/3 mod 7 =(a) 2(b) 3(c) 4(d) 5The question was posed to me during a job interview.I want to ask this question from Polynomial and Modular Arithmetic- III in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT choice is (c) 4 The EXPLANATION: 5/3 MOD 7 = (5×3^-1) mod 7 = (5×5) mod 7 = 4.

52.	A Ring is said to be commutative if it also satisfies the property(a) R-vi(b) R-v(c) R-vii(d) R-ivI had been asked this question during an interview.Origin of the question is Groups Rings and Fields topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT CHOICE is (d) R-iv To EXPLAIN I WOULD say: A Ring is SAID to be commutative if it also satisfies the property R-iv: Commutativity of multiplication.

53.	The multiplicative Inverse of 1234 mod 4321 is(a) 3239(b) 3213(c) 3242(d) Does not existThe question was asked in an interview.I want to ask this question from Number Theory topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT OPTION is (a) 3239 Explanation: The MULTIPLICATIVE Inverse of 1234 MOD 4321 is 3239.

54.	The GCD of x^5+x^4+x^3 – x^2 – x + 1 and x^3 + x^2 + x + 1 over GF(3) is(a) 1(b) x(c) x + 1(d) x^2 + 1I had been asked this question during a job interview.Query is from Polynomial and Modular Arithmetic- IV in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT answer is (C) x + 1 To EXPLAIN I would say: The GCD of x^5+x^4+x^3 – x^2 – x + 1 and x^3 + x^2 + x + 1 over GF(3) is x + 1.

55.	Find the inverse of (x^5) modulo (x^8+x^4 +x^3+ x + 1).(a) x^5+ x^4+ x^3+x+1(b) x^5+ x^4+ x^3(c) x^5+ x^4+ x^3+1(d) x^4+ x^3+x+1I had been asked this question in my homework.The above asked question is from Polynomial and Modular Arithmetic topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right CHOICE is (c) X^5+ x^4+ x^3+1 The BEST explanation: Finding the inverse with respect to (x^8+x^4 +x^3+ x + 1) we get x^5+ x^4+ x^3+1 as the inverse.

56.	On multiplying (x^5 + x^2 + x) by (x^7 + x^4 + x^3 + x^2 + x) in GF(28) with irreducible polynomial (x^8 + x^4 + x^3 + x + 1) we get(a) x^12+x^7+x^2(b) x^5+x^3+x^3(c) x^5+x^3+x^2+x(d) x^5+x^3+x^2+x+1I had been asked this question in examination.I'm obligated to ask this question of Polynomial and Modular Arithmetic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct ANSWER is (d) x^5+x^3+x^2+x+1 Explanation: MULTIPLICATION gives us (x^12 + x^7 + x^2) MOD (x^8 + x^4 + x^3 + x + 1). REDUCING this via modular division gives us, (x^5+x^3+x^2+x+1)

57.	If f(x)=x^7+x^5+x^4+x^3+x+1 and g(x)=x^3+x+1, find the quotient of f(x) / g(x).(a) x^4+x^3+1(b) x^4+1(c) x^5+x^3+x+1(d) x^3+x^2This question was addressed to me in class test.I'm obligated to ask this question of Polynomial and Modular Arithmetic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct CHOICE is (b) x^4+1 The EXPLANATION: Perform MODULAR Division.

58.	If f(x)=x^4+x^2-x+2 and g(x)=x^2-x+1, find: f(x) – g(x)(a) x^4+1(b) x^2+1(c) x^2+2x+6(d) x^4-1This question was addressed to me during a job interview.This is a very interesting question from Polynomial and Modular Arithmetic- I topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct option is (a) x^4+1 For EXPLANATION I would SAY: Perform POLYNOMIAL SUBTRACTION.

59.	If f(x)=x^3+x^2+2 and g(x)=x^2-x+1, find: f(x) – g(x)(a) x^3+x+4(b) x^3+x+1(c) x^3+x^2+3(d) x^3+3x+2I got this question during an online interview.The doubt is from Polynomial and Modular Arithmetic- I topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct choice is (b) x^3+x+1 Explanation: We GET the SOLUTIONS VIA basic polynomial SUBTRACTION.

60.	Multiplication / Division follow which operation?(a) XOR(b) NAND(c) AND(d) ORThis question was posed to me by my school principal while I was bunking the class.The query is from Polynomial and Modular Arithmetic- I in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct CHOICE is (c) AND To ELABORATE: MULTIPLICATION / Division is the same as the AND operations.

61.	a.(b.c) = (a.b).c is the representation for which property?(a) G-ii(b) G-iii(c) R-ii(d) R-iiiThe question was posed to me in an internship interview.I would like to ask this question from Groups Rings and Fields in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct OPTION is (a) G-ii To explain I would SAY: a.(b.c) = (a.b).c REPRESENTS the ASSOCIATIVE PROPERTY.

62.	All groups satisfy properties(a) G-i to G-v(b) G-i to G-iv(c) G-i to R-v(d) R-i to R-vThe question was posed to me during an interview.I would like to ask this question from Groups Rings and Fields topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT option is (b) G-i to G-iv For EXPLANATION I would say: Group G denoted by {G,o}, is a SET of ELEMENTS that satisfy the properties G-i to G-iv.

63.	In modular arithmetic : (a/b) = b(a^-1)(a) True(b) FalseI had been asked this question by my school teacher while I was bunking the class.The question is from Groups Rings and Fields in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT choice is (b) False To ELABORATE: This statement is not true. The correct version WOULD be : (a/b) = a(b^-1).

64.	Is x^4 + 1 reducible over GF(2)(a) Yes(b) No(c) Can’t Say(d) Insufficient DataThe question was asked by my school teacher while I was bunking the class.My question is taken from Polynomial and Modular Arithmetic- IV topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right answer is (a) Yes For EXPLANATION: REDUCIBLE: (X + 1)^4.

65.	The GCD of x^3+ x + 1 and x^2 + x + 1 over GF(2) is(a) 1(b) x + 1(c) x^2(d) x^2 + 1I have been asked this question during an online exam.Query is from Polynomial and Modular Arithmetic- IV topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer»

66.	Find the 8-bit word related to the polynomial x^5 + x^2 + x(a) 00010011(b) 01000110(c) 00100110(d) 11001010I had been asked this question in unit test.My question is based upon Polynomial and Modular Arithmetic- I in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT OPTION is (c) 00100110 Easy explanation: The RESPECTIVE 8-bit word is 00100110.

67.	GCD(a,b) = GCD(b,a mod b)(a) True(b) FalseI had been asked this question by my college director while I was bunking the class.My doubt is from Groups Rings and Fields in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT ANSWER is (a) TRUE Easiest explanation: The STATEMENT is true. For example, GCD(55,22) = GCD(22,55 mod 22) = GCD(22,11) = 11

68.	The multiplicative Inverse of 24140 mod 40902 is(a) 2355(b) 5343(c) 3534(d) Does not existThis question was posed to me during an online interview.My doubt is from Number Theory in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The CORRECT option is (d) Does not exist The BEST EXPLANATION: The multiplicative Inverse does not exist as GCD (24140, 40902) = 34.