The RSA (Rivest-Shamir-Adleman) algorithm is a widely used asymmetric cryptosystem. Its security is fundamentally based on the computational difficulty of the integer factorization problem. The public key consists of a modulus n (the product of two large, secret prime numbers) and a public exponent e. To derive the corresponding private key, an attacker would need to determine the original prime factors of n. For sufficiently large numbers, factoring n is computationally infeasible with current technology, which ensures the security of the private key.

A. El Gamal: Its security is based on the difficulty of solving the Discrete Logarithm Problem (DLP) over a finite field.
B. Elliptic Curve Cryptosystems (ECCs): Security relies on the Elliptic Curve Discrete Logarithm Problem (ECDLP), a more complex variant of the DLP.
D. International Data Encryption Algorithm (IDEA): This is a symmetric-key block cipher and does not use the principles of asymmetric cryptography like factoring or discrete logarithms.

1. Paar, C., & Pelzl, J. (2010). Understanding Cryptography: A Textbook for Students and Practitioners. Springer. In Chapter 6, Section 6.2, "The RSA Cryptosystem," it is stated: "The security of RSA relies on the fact that it is difficult to factor large integers." (p. 161).

2. Katz, J., & Lindell, Y. (2014). Introduction to Modern Cryptography (2nd ed.). CRC Press. Chapter 11, Section 11.3, "The RSA Assumption," directly connects the security of the RSA cryptosystem to the hardness of the factoring problem. (p. 378).

3. National Institute of Standards and Technology (NIST). (2013). FIPS PUB 186-4: Digital Signature Standard (DSS). Section 5.1.1, "RSA Key Pair Generation," details the process where the modulus n is the product of two secret primes, p and q, establishing that the security relies on the secrecy of these factors. (DOI: https://doi.org/10.6028/NIST.FIPS.186-4).

4. Boneh, D. (1999). Twenty Years of Attacks on the RSA Cryptosystem. Notices of the American Mathematical Society, 46(2), 203-213. The paper's introduction states, "The security of the RSA system is based on the assumption that factoring a large number is difficult." (p. 203).