-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Andrew Del Vecchio wrote: > That's cool are you working on sample code at this time? > > ~Andrew > > Watson Ladd wrote: >> Andrew Del Vecchio wrote: >>> What are "eliptic curves", Watson? I'm not a math master, I just >>> know how to do IT :D >>> ~Andrew >> Elliptic curves are equations of the form y^2=x^3+ax+b. In >> cryptography we consider them over the projective plane formed by a >> finite field, and we can add points on the curve to form cyclic >> subgroups for which the Diffie-Hellman problem is hard. The main >> advantage is a major speedup, and key sizes can be smaller for the >> same security factor. There are a lot of patents involved, meaning >> you need to pay care to how you are doing the math. But the prize >> is very good security, as no breakthroughs have been made since >> 1985. Check the wiki for details. >>> Watson Ladd wrote: >>>> Jason Holt wrote: >>>>> On Fri, 1 Sep 2006, Watson Ladd wrote: >>>>>> I have a good idea for key negotiations (NOTE:UNPUBLISHED). >>>>>> Here >>>> it is: >>>>>> Let the server have a public key y=h^x mod p, p=2q+1, >>>>>> h=g^2, and >>>> private >>>>>> key x^-1 mod q, or z. (g is a generator). >>>>>> >>>>>> A client will send y^a and remember a. A server will send >>>>>> back h^b and remember b. The client will compute (h^b)^a. >>>>>> The server will compute (y^a)^(bz). We note that: >>>>>> (y^a)^(bz)=h^(ax*bz)=h^(abxz)=h^(ab)=(h^b)^a, as z and x >>>>>> are multiplicative inverses mod q. We further note that >>>>>> this is just Diffie-Hellman if we replace y with h^z, a >>>>>> with a*x, and z with 1, b with b. So this is secure if >>>> DDH holds. >>>>>> I am not a cryptographer, so will someone please check this >>>>>> method. I have not found it anywhere. >>>>> Why would we use this instead of plain-vanilla >>>>> Diffie-Hellman? -J >>>> To authenticate the server to the client. I want to dispense >>>> with RSA as we are putting a critical egg into two baskets at >>>> once. Also, we can migrate to exotic DDH assumption groups if a >>>> breakthrough happens. Like GF(p^n), n>1, or elliptic curves. > No. A full proof. Sample code does not matter if it's an insecure protocol. My presentation needs to be made a lot tighter first. - -- They who would give up an essential liberty for temporary security, deserve neither liberty or security - --Benjamin Franklin -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.3 (Darwin) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org
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