Correctness in Multi-party Computation: Real/Ideal Paradigm in Malicious case I need to know:

1- What does exactly correctness mean in this context?

2- How is correctness implied in malicious model? 

3- If the correctness means " the adversary cannot cause the output to be incorrectly distributed"[1] then it can change the computation result with the correct distribution.



[1].Carmit Hazay · Yehuda Lindell,Efficient Secure Two-Party
Protocols,Techniques and Constructions.
1- $\:$ I believe correctness does not have an exact meaning in this context.

It would certainly involve not letting the distinguisher see the transcript,

and might involve not letting the distinguisher see the adversary's randomness,

and possibly involved not even letting the distinguisher see the auxiliary input.

2- $\:$ [Computational/Statistical/Perfect] correctness is implied by

[computational/statistical/perfect] indistinguishability of the Real and Ideal cases,

since the distinguisher gets to see the honest parties' outputs.