1. A process of operating a computer system comprising: A. receiving a cryptographic signature in a memory in an unsecure environment of the computer system; B. determining whether the received cryptographic signature is identical to a previously received signature, which is stored in a signature cache in a secure execution environment of the computer system; C. if no identical previously received signature is located in the signature cache, i. applying, in the secure execution environment, cryptographic primitives of the digital signature verification scheme agreed to be employed on messages between signer to the received cryptographic signature in a digital signature scheme calculator in the secure execution environment, and ii. adding a copy of the results of application of the appropriate cryptographic primitives as a new entry to the signature cache; and D. if an identical previously received signature is located in the signature cache, i. retrieving, in the secure execution environment, the stored results of the previous utilization of cryptographic primitives corresponding to the relevant digital signature scheme being employed, which results were previously stored at an identified location in the signature cache, ii. applying a hash value to the cryptographic signature, iii. comparing a hash value of the cryptographic signature generated by a hash function with a hash value retrieved from the signature cache, and iv. if there is a match, verifying the cryptographic signature and any message accompanying the cryptographic signature.