Final answer:
Upgrading the cipher suite to use an authenticated AES mode of operation would most likely improve the enterprise's resilience to attacks on cryptographic implementation.
Step-by-step explanation:
The technique that would MOST likely improve the resilience of the enterprise to attack on cryptographic implementation is to Upgrade the cipher suite to use an authenticated AES mode of operation. Upgrading the cipher suite to use an authenticated AES mode of operation provides stronger security by adding an authentication mechanism to the encryption process, ensuring the integrity and authenticity of the encrypted data. This would help prevent malicious nation-state-sponsored activities from successfully targeting the use of encryption between the sites.
The other options, such as adding a second-layer VPN, using a stronger elliptic curve cryptography algorithm, implementing an IDS with sensors, or keeping cryptography modules up to date, may provide some additional security measures, but upgrading the cipher suite to use an authenticated AES mode of operation would have the most significant impact on improving the resilience of the enterprise to attack on cryptographic implementation.