The security of RSA public-key encryption is based on the hardness of _______.

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To evaluate the security basis of RSA public-key encryption, we need to consider the underlying mathematical hardness that makes breaking RSA computationally difficult.
Option a: primality checking problem. While primality testing is important in number theory and RSA key generation requires selecting primes, the security of RSA does not rely on primality checking itself being hard. It relies on the difficulty of a related problem after the primes are chosen.
Option b: GCD problem. Computing the greatest common divisor can be done efficiently with modern algorithms, and it is not the core hardness that RSA depends on. RSA security does not rest on the difficulty of GCD computations.
Option c: discrete logarithm problem. The discrete log problem is central to the security of other cryptosystems (like Diffie-Hellman or DSA), but RSA’s security model is different. RSA does not rely on the hardness of discrete logs.
Option d: integer factorisation problem. This is the foundational hardness assumption for RSA: given a large composite number that is the product of two (or sometimes more) primes, factoring it into the original primes is believed to be computationally infeasible for appropriately chosen key sizes. This factoring problem makes deriving the private key from the public key extremely hard, which is why RSA works as a public-key system.
In summary, among the listed options, the integer factorisation problem best matches the security basis of RSA, reflecting the core challenge an attacker would face to recover the private key from the public key.

FIT1093_S2_2025 Week 5 MCQ: Public Key Cryptography Part 2

The security of RSA public-key encryption is based on the hardness of _______.

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