Service A hashes a message, resulting in message digest X. Service A encrypts message digest X with its private key, resulting in cipher text X1…

Service A hashes a message, resulting in message digest X. Service A encrypts message digest X with its private key, resulting in cipher text X1. Service A sends the message and X1 to Service B. Service B hashes the message, resulting in message digest Y. Service B decrypts X1 with Service A's public key, recovering message digest X1. Service B compares X and Y and finds them not to be equal. This proves that;