### Question regarding common modulus on elliptic curve cryptosystems

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.

### Re: Question regarding common modulus on elliptic curve cryptosystems

[Moderator's Note: please don't top post... --Perry] Sounds like a bad idea -- at a minimum, your encryption will be deterministic. What are you actually trying to achieve? Usually once you understand that, you can find a protocol solving your problem already in the crypto literature. On

### Re: Question regarding common modulus on elliptic curve cryptosystems

Hi, Elliptic Curve Pohlig-Hellman is comutative. It's quite simple. I've implemented it. Regards, Zacheusz Siedlecki 2010/3/21 Sergio Lerner sergioler...@pentatek.com: I looking for a public-key cryptosystem that allows commutation of the operations of

### Re: Question regarding common modulus on elliptic curve cryptosystems

[Moderator's Note: please don't top post --Perry] Commutativity is a beautiful and powerful property. See On the power of Commutativity in Cryptography by Adi Shamir. Semantic security is great and has given a new provable sense of security, but commutative building blocks can be combined

### Re: Question regarding common modulus on elliptic curve cryptosystems

As far as I understand, Elliptic Curve Pohlig-Hellman is not public-key. It's a private key cipher. Regards, Sergio. On 22/03/2010 09:56 a.m., Zacheusz Siedlecki wrote: Hi, Elliptic Curve Pohlig-Hellman is comutative. It's quite simple. I've implemented it. Regards,

### Re: Question regarding common modulus on elliptic curve cryptosystems

[Moderator's Note: Please please don't top post. --Perry] That paper was from 1980. A few things have changed since then. =) In any case, my point still stands: what you actually want is some e-cash system with some special properties. Commutative encryption is neither necessary nor

### Re: Question regarding common modulus on elliptic curve cryptosystems AND E-CASH

I've read some papers, not that much. But I don't mind reinventing the wheel, as long as the new protocol is simpler to explain. Reading the literature, I couldn't find a e-cash protocol which : - Hides the destination / source of payments. - Hides the amount of money transferred. - Hides the

### Re: Question regarding common modulus on elliptic curve cryptosystems

[Moderator's note. Please please please don't top post. --Perry] I think you should look for multisignature schemes. There are lots of it. And BTW - right EC Pohlih-Hellman is not public key cryptosystem. I missed your requirement. Regards, Zacheusz 2010/3/22,