Named after its inventors Ron Rivest , Adi Shamir and Leonard Adleman is based on the difficulty of factoring large prime numbers.
Factoring a number means representing it as the product of prime numbers. Prime numbers, such as 2, 3, 5, 7, 11, and 13, are those numbers that are not evenly divisible by any smaller number, except 1. A non-prime, or composite number, can be written as the product of smaller primes, known as its prime factors. 665, for example is the product of the primes 5, 7, and 19. A number is said to be factored when all of its prime factors are identified. As the size of the number increases, the difficulty of factoring increases rapidly.
The other answers are incorrect because:
El Gamal is based on the discrete logarithms in a finite field.
Elliptic Curve Cryptosystems (ECCs) computes discrete logarithms of elliptic curves.
International Data Encryption Algorithm (IDEA) is a block cipher and operates on 64 bit blocks of data and is a SYMMETRIC algorithm.
Reference : Shon Harris , AIO v3 , Chapter-8 : Cryptography , Page : 638
