Mental poker is the common description for a set of cryptographic problems related to playing a fair game over a distance without the need for any trusted third party.

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Cryptographic system with double keys with reversible order

While reading Shamir, Rivest and Adleman's paper on "Mental Poker", I've met a mention of system such that $E_a(E_b(x)) = E_b(E_a(x))$, without however disclosing details on it, with $E_a(x)$ being ...
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Is there a public key semantically secure cryptosystem for which one can prove in zero knowledge the equivalence of two plaintexts?

If Alice encrypts two messages $a$ and $b$, such that $x=E(a)$, $y=E(b)$. Can Alice prove (without revealing $a$, $b$ or the private key) that $a = b$? Obviously the proof must not be too long and it ...
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How to secure a mental poker protocol? [closed]

I would like to implement a mental poker protocol in a secure fashion. How should I go about that without (preferably) infringing on the Mental Poker Framework patent?