ITPEC FE Subject A April 2024 Question 29
Which of the following is a public-key cryptography algorithm whose security depends on the difficulty of factoring extremely large numbers into primes?
Explanation
RSA — its security rests on how hard it is to factor the product of two very large primes.
RSA's public key includes a modulus n = p × q, where p and q are large secret primes. Multiplying them is easy, but recovering p and q from n is infeasible for keys of adequate length, and anyone who could factor n could compute the private key.
Answer (d)
Why not others:
- •(a) AES — a symmetric (common-key) block cipher, not public-key cryptography, and not based on factoring
- •(b) DH — Diffie-Hellman key exchange is public-key, but its security depends on the discrete logarithm problem
- •(c) DSA — the Digital Signature Algorithm is also based on the discrete logarithm problem, not factoring
Key rule: Tie each public-key algorithm to its hard problem: prime factorization is RSA; discrete logarithm is Diffie-Hellman and DSA; elliptic-curve discrete logarithm is ECC.
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