<p>This got a bit too long for a comment, I might edit this to provide a more coherent answer at a later point.
There is this answer to <a href="https://crypto.stackexchange.com/questions/52828/is-it-possible-to-construct-an-encryption-scheme-for-which-breaking-is-np-comple/52833#52833">Is it possible to construct an encryption scheme for which breaking is NP complete but there nearly always exists an efficient breaking algorithm</a> on crypto stackexchange. It argues, we want hard problems for encryption to be in both NP and coNP. So I would say we might have some hope for designing actually good cryptosystems from NP-complete problems instead of having to design them from problems in that intersection. See <a href="https://cstheory.stackexchange.com/questions/49/consequences-of-complete-problems-for-np-intersects-conp">here</a> for what we know about possibility of complete problems for the intersection.</p>

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2022-07-14T13:52:17.570Z
2022-07-14T14:27:41.427Z
2022-07-14T14:27:41.427Z
Ilk
<p>Are there any major implications of NP = coNP (if true) the way there would be if P=NP? I'm thinking of real-world implications analogous to the encryption-pocalypse (excuse the drama) that would happen if P=NP.</p>

<cc.complexity-theory><np><p-vs-np>
What if NP = coNP?
Würthi
# What if NP = coNP?

(Asked by: username_0 on 2022-07-14)

Are there any major implications of NP = coNP (if true) the way there would be if P=NP? I'm thinking of real-world implications analogous to the encryption-pocalypse (excuse the drama) that would happen if P=NP.

**Tags:** cc.complexity-theory, np, p-vs-np


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## 1 answers

### Answer by username_1 on 2022-07-14. Score: 3 | Accepted answer

This got a bit too long for a comment, I might edit this to provide a more coherent answer at a later point.
There is this answer to [Is it possible to construct an encryption scheme for which breaking is NP complete but there nearly always exists an efficient breaking algorithm](https://crypto.stackexchange.com/questions/52828/is-it-possible-to-construct-an-encryption-scheme-for-which-breaking-is-np-comple/52833#52833) on crypto stackexchange. It argues, we want hard problems for encryption to be in both NP and coNP. So I would say we might have some hope for designing actually good cryptosystems from NP-complete problems instead of having to design them from problems in that intersection. See [here](https://cstheory.stackexchange.com/questions/49/consequences-of-complete-problems-for-np-intersects-conp) for what we know about possibility of complete problems for the intersection.


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