Final answer:
Conditions to quickly rule out CPA security include the presence of large prime numbers, rapid computation using quantum algorithms, and the utilization of public-key cryptography.
Step-by-step explanation:
Presence of large prime numbers in the encryption algorithm can indicate that the scheme is not CPA (Chosen-Plaintext Attack) secure. CPA security requires that different plaintexts encrypt to different ciphertexts. If large prime numbers are present, the encryption may not have the desired level of randomness and could potentially lead to vulnerabilities. Rapid computation using quantum algorithms is another condition that may quickly rule out CPA security. Quantum computers have the potential to solve certain mathematical problems much faster, which could potentially break the encryption scheme. Utilization of public-key cryptography does not guarantee CPA security. Public-key cryptography is more commonly associated with other types of security properties, such as providing confidentiality, integrity, and authentication. Therefore, the presence of public-key cryptography alone does not ensure CPA security.