Question regarding common modulus on elliptic curve cryptosystems

[Matt Crawford]

On Mar 21, 2010, at 4:13 PM, Sergio Lerner wrote:

> I looking for a public-key cryptosystem that allows commutation of the operations of encription/decryption for different users keys
> ( Ek(Es(m)) =  Es(Ek(m)) ).
> I haven't found a simple cryptosystem in Zp or Z/nZ.
> 
> I think the solution may be something like the RSA analogs in elliptic curves. Maybe a scheme that allows the use of a common modulus for all users (RSA does not).

If your application can work with a trusted authority generating all the keypairs, and you sacrifice the use of short public exponents *and* sacrifice the possession of the factors of the modulus by the key owners, making them do more work on decryption, I think you can have what you asked for. But that's a lot of ifs.

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