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Which of the following asymmetric encryption algorithms…

Which of the following asymmetric encryption algorithms is based on the difficulty of factoring LARGE
numbers?

PrepAway - Latest Free Exam Questions & Answers

A.
El Gamal

B.
Elliptic Curve Cryptosystems (ECCs)

C.
RSA

D.
International Data Encryption Algorithm (IDEA)

Explanation:
RSA is derived from the last names of its inventors, Rivest, Shamir, and Addleman.
This algorithm is based on the difficulty of factoring a number, N, which is the product of two large prime
numbers. These numbers may be 200 digits each. Thus, the difficulty in obtaining the private key from the
public key is a hard, one-way function that is equivalent to the difficulty of finding the prime factors of N.
In RSA, public and private keys are generated as follows:
Choose two large prime numbers, p and q, of equal length, compute p3q 5 n, which is the public modulus.
Choose a random public key, e, so that e and (p – 1)(q – 1) are relatively prime.
Compute e x d = 1 mod (p – 1)(q – 1), where d is the private key.
Thus, d = e–1 mod [(p – 1)(q – 1)]
From these calculations, (d, n) is the private key and (e, n) is the public key.
Incorrect Answers:
A: El Gamal is based not on the difficulty of factoring large numbers but on calculating discrete logarithms in a
finite field.
B: Elliptic Curve Cryptosystems (ECCs) are not based on the difficulty of factoring large numbers.
D: International Data Encryption Algorithm (IDEA) is not based on the difficulty of factoring large numbers.

Krutz, Ronald L. and Russel Dean Vines, The CISSP Prep Guide: Mastering the Ten Domains of Computer
Security, John Wiley & Sons, New York, 2001, p. 148


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