Which algorithm is based on the difficulty of factoring large integers?

Which algorithm is based on the difficulty of factoring large integers?

• A. RSA Cryptosystem
• B. Advanced Encryption Standard
• C. Digital Signature Algorithm
• D. Hash Function

Answer: (A)

This question tests understanding that RSA’s security rests on the difficulty of factoring large integers. In RSA, you pick two large primes and multiply them to form n. The public key uses n and an exponent e, while the private key is derived from the inverse of e modulo φ(n). If someone could factor n into p and q, they could compute φ(n) and then derive the private key, breaking the system. The security therefore hinges on factoring large semiprimes being impractical with current methods. Other options don’t fit because AES is a symmetric-key encryption algorithm, not based on factoring; DSA relies on the difficulty of the discrete logarithm problem; and hash functions are one-way digests, not encryption schemes dependent on factoring.

This question tests understanding that RSA’s security rests on the difficulty of factoring large integers. In RSA, you pick two large primes and multiply them to form n. The public key uses n and an exponent e, while the private key is derived from the inverse of e modulo φ(n). If someone could factor n into p and q, they could compute φ(n) and then derive the private key, breaking the system. The security therefore hinges on factoring large semiprimes being impractical with current methods.

Other options don’t fit because AES is a symmetric-key encryption algorithm, not based on factoring; DSA relies on the difficulty of the discrete logarithm problem; and hash functions are one-way digests, not encryption schemes dependent on factoring.