Final answer:
The most crucial service provided by a cryptosystem for the military is confidentiality, protecting sensitive information from being accessed by adversaries.
Step-by-step explanation:
For the military, the most important service provided by a cryptosystem is likely confidentiality. Confidentiality ensures that sensitive information such as troop movements, strategies, and classified technologies are kept secret from adversaries. While authentication, nonrepudiation, and integrity are also critical aspects of a secure cryptosystem, the paramount concern for the military is ensuring that intelligence remains out of the hands of the enemy. Any leak of such information could have potentially catastrophic consequences for national security and operational effectiveness. Cryptosystems are designed to encrypt data, making it unreadable to anyone without the proper decryption key, thus preserving the confidentiality of the information.