Question regarding common modulus on elliptic curve cryptosystems

Jonathan Katz jkatz at
Mon Mar 22 09:25:03 EDT 2010

[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 (probably) sufficient for what you want. Have you at least 
looked at the literature (which must be well over 100 papers) on e-cash?

On Mon, 22 Mar 2010, Sergio Lerner wrote:

> 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 to build the strangest 
> protocols without going into deep mathematics, are better suited for teaching 
> crypto and for high-level protocol design. They are like the "Lego" blocks of 
> cryptography!
> Now I'm working on an new untraceable e-cash protocol which has some 
> additional properties. And I'm searching for a secure  commutable signing 
> primitive.
> Best regards,
> Sergio Lerner.
> On 22/03/2010 09:56 a.m., Jonathan Katz wrote:
>> 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 Sun, 21 Mar 2010, 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).
>>> I've read on some factoring-based cryptosystem (like Meyer-Muller or 
>>> Koyama-Maurer-Okamoto-Vantone) but the cryptosystem authors say nothing 
>>> about the possibility of using a common modulus, neither for good nor for 
>>> bad.
>>> Anyone has a deeper knowledge on this crypto to help me?
>>> Best regards,
>>> Sergio Lerner.
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