# 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.

• If this is the case, in multi-party computation in malicious model, when the model guarantees the correctness of output? So my main question is: How does this model capture the correctness of output that is received by an honest party? Commented Jun 3, 2015 at 8:38
• This model captures "the correctness of output that is received by an honest party" by letting the distinguisher "see the honest parties' outputs." $\:$ I can't figure out how to parse the other sentence in your comment. $\;\;\;\;$
– user991
Commented Jun 3, 2015 at 8:59
• Thanks for the previous answers. Am I right to say it'd mean if a corrupted party provides a wrong input, the distinguisher cannot distinguish an honest party's output in the real world from its output in the ideal world? Finally, could you refer me to a textbook (other than foundation of cryptography by Oded Goldrich) that explains the model in a clear way, please. Commented Jun 3, 2015 at 9:21
• Yes. $\:$ (The same applies "if a corrupted party provides a" right input, whatever that may mean.) $\hspace{.56 in}$ Huh, I can't seem to find any good books on the model. $\;\;\;\;$
– user991
Commented Jun 3, 2015 at 9:52
• CAn I ask you please why the adversary $A$ is defined as "non-uniform" PPT rather than simply PPT ? Commented Jun 3, 2015 at 11:01