In some security proofs it is stated that "a protocol securely realizes an ideal functionality" while in some others "a protocol securely implements an ideal functionality".
- Is there a meaningful difference or it is just another verb to say a similar thing?
- Also, is there any difference between emulation and simulation in the context of MPC?
Example for question 1: Outsourced pattern matching, S. Faust, et al. see Definition 3 and compare with 5PM: secure pattern matching, J. Baron, et al. page 29 definition 5.
Example for question 2: wikipedia article on Universal composability:
Literally, the protocol may simulate the other protocol (without having access to the code). The notion of security is derived by implication. Assume a protocol P_1 is secure per definition. If another protocol P_2 emulates protocol P_1 such that no environment tells apart the emulation from the execution of the protocol, then the emulated protocol P_2 is as secure as protocol P_1.