This set of Cryptography Multiple Choice Questions & Answers (MCQs) focuses on “Groups Rings and Fields”.

1. GCD(a,b) = GCD(b,a mod b)

a) True

b) False

View Answer

Explanation: The statement is true. For example, GCD(55,22) = GCD(22,55 mod 22) = GCD(22,11) = 11

Consider the Following properties Properties

G-i) Closure

G-ii) Associative

G-iii) Identity Element

G-iv) Inverse Element

G-v) Commutative

Consider the Following properties Properties

R-i) Closure under multiplication

R-ii) Associativity of multiplication

R-iii) Distributive Law

R-iv) Commutativity of multiplication

R-v) Multiplicative Identity

R-vi) No zero divisors

R-vii) Multiplicative Inverse

2. 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-v

View Answer

Explanation: Group G denoted by {G,o}, is a set of elements that satisfy the properties G-i to G-iv.

3. An Abelian Group satisfies the properties

a) G-i to G-v

b) G-i to R-iv

c) G-i to R-v

d) R-i to R-v

View Answer

Explanation: An Abelian group is a group that satisfies the Commutative property also.

4. A Ring satisfies the properties

a) R-i to R-v

b) G-i to G-iv

c) G-i to R-v

d) G-i to R-iii

View Answer

Explanation: A ring R denoted by {R, + , x} is a set of elements with two binary operations addition and multiplication and satisfy axioms G-i to R-iii.

5. A Ring is said to be commutative if it also satisfies the property

a) R-vi

b) R-v

c) R-vii

d) R-iv

View Answer

Explanation: A Ring is said to be commutative if it also satisfies the property R-iv: Commutativity of multiplication.

6. An ‘Integral Domain’ satisfies the properties

a) G-i to G-iii

b) G-i to R-v

c) G-i to R-vi

d) G-i to R-iii

View Answer

Explanation:An ‘Integral Domain’ satisfies the properties G-i to R-vi.

7. A Field satisfies all the properties above from G-i to R-vi.

a) True

b) False

View Answer

Explanation: A Field satisfies all the properties above from G-i to R-vi and is denoted by {F, +, x}.

8. In modular arithmetic : (a/b) = b(a^-1)

a) True

b) False

View Answer

Explanation: This statement is not true. The correct version would be : (a/b) = a(b

^{-1}).

9. a.(b.c) = (a.b).c is the representation for which property?

a) G-ii

b) G-iii

c) R-ii

d) R-iii

View Answer

Explanation: a.(b.c) = (a.b).c represents the Associative property.

10. a(b+c) = ac+bc is the representation for which property?

a) G-ii

b) G-iii

c) R-ii

d) R-iii

View Answer

Explanation: a(b+c) = ac+bc represents the Distributive Property.

11. For the group Sn of all permutations of n distinct symbols, what is the number of elements in Sn?

a) n

b) n-1

c) 2n

d) n!

View Answer

Explanation: There there are n distinct symbols there will be n! elements.

12. For the group Sn of all permutations of n distinct symbols, Sn is an abelian group for all values of n.

a) True

b) False

View Answer

Explanation: For n>2 it does not form a Abelian Group.

13. Is S a ring from the following multiplication and addition tables?

+ a b x a b

a a b a a a

b b a b a b

a) Yes

b) No

c) Can’t Say

d) Insufficient Data

View Answer

Explanation: S is a ring as it satisfies the properties G-i to R-iii.

14. Does the set of residue classes (mod 3) form a group with respect to modular addition?

a) Yes

b) No

c) Can’t Say

d) Insufficient Data

View Answer

Explanation: Yes. The identity element is 0, and the inverses of 0, 1, 2 are respectively 0, 2, 1.

15. Does the set of residue classes (mod 3) form a group with respect to modular addition?

a) Yes

b) No

c) Can’t Say

d) Insufficient Data

View Answer

Explanation: No. The identity element is 1, but 0 has no inverse.

**Sanfoundry Global Education & Learning Series – Cryptography and Network Security.**

To practice all areas of Cryptography and Network Security, __here is complete set of 1000+ Multiple Choice Questions and Answers__