Cryptographic Algorithms Quiz

What algebraic structures are used in cryptographic algorithms such as RSA and El Gamal?

• Linear equations and matrices

• Group structures and modular arithmetic

• Differential equations and integrals

• Permutations and combinations

What is the particular form of the Integer Factorisation Problem (IFP) that RSA works with?

• n = p + q where p and q are prime numbers

• n = pq where p and q are composite numbers

• n = p - q where p and q are prime numbers

• n = pq where p and q are prime numbers

What do we employ in the El Gamal Algorithm to deal with the Discrete Logarithm Problem?

• Linear groups and their primitives

• Cyclic groups and their primitives

• Symmetric groups and their operations

• Infinite groups and their properties

What does the Closure Law in group theory state?

• For all a, b in G, there exists an element c in G such that a * b = c

• For all a, b in G, a * b = b * a

• For all a, b in G, a * (b * c) = (a * b) * c

• There exists an element e in G such that for all a in G, a * e = e * a = a

Which law is expressed by the equation a * (b * c) = (a * b) * c?

• Closure Law

• Associative Law

• Commutative Law

• Identity Law

What is the Identity Law in group theory?

What does the Inverse Law state in the context of group theory?

• For all a, b in G, a * b = b * a

• For all a in G, there exists an element b in G such that a * b = b * a = e

• For all a in G, there exists an element b in G such that a * b = e

• For all a in G not equal to 0, there exists an element b in G such that a * b^-1 = b^-1 * a = e

According to the Commutative Law, which of the following is true for all a, b in a group G?

• a * (b * c) = (a * b) * c

• There exists an element e in G such that for all a in G, a * e = e * a = a

• For all a in G, there exists an element b in G such that a * b = e

• a * b = b * a

What is required for a set G with an operator * to be considered a Group?

• It must satisfy properties (1) - (4).

• It must satisfy property (5) only.

• It must contain at least one element.

• It must be named after a mathematician.

What additional property must a group (G, *) satisfy to be considered an Abelian Group?

• It must satisfy property (1) only.

• It must satisfy property (5).

• It must be infinite.

• It must be named after Nils Abel.