Comments on: key-compression http://www.neverendingbooks.org/index.php/key-compression.html lieven le bruyn's blog Fri, 20 Jan 2012 16:50:41 +0100 hourly 1 http://wordpress.org/?v=3.3.1 By: Writing & Blogging | neverendingbooks http://www.neverendingbooks.org/index.php/key-compression.html/comment-page-1#comment-9466 Writing & Blogging | neverendingbooks Tue, 07 Dec 2010 13:14:23 +0000 http://www.neverendingbooks.org/?p=241#comment-9466 [...] I would blog only after having digested the material myself… Typical recent examples are the tori-crypto-posts and the Bost-Connes algebra [...] [...] I would blog only after having digested the material myself… Typical recent examples are the tori-crypto-posts and the Bost-Connes algebra [...]

]]> By: ECSTR aka XTR | neverendingbooks http://www.neverendingbooks.org/index.php/key-compression.html/comment-page-1#comment-3860 ECSTR aka XTR | neverendingbooks Sat, 05 Jan 2008 14:00:23 +0000 http://www.neverendingbooks.org/?p=241#comment-3860 <p>[...] Table of contents for rationality & cryptographytori & crypto : Diffie-Hellman or GCHQ?key-compressionECSTR aka [...]</p> [...] Table of contents for rationality & cryptographytori & crypto : Diffie-Hellman or GCHQ?key-compressionECSTR aka [...]

]]> By: Michel Van den Bergh http://www.neverendingbooks.org/index.php/key-compression.html/comment-page-1#comment-3819 Michel Van den Bergh Fri, 04 Jan 2008 16:34:25 +0000 http://www.neverendingbooks.org/?p=241#comment-3819 <p>Perhaps you should point out that DH key exchange makes sense in ANY group for which the discrete logarithm problem is hard. One popular choice is the group of rational points on an elliptic curve (ECC). Another possible choice is apparently the group of rational points on a torus.</p> <p>Of course there are no groups for which the DL problem has been PROVED to be hard. </p> <p>Rationality is not really necessary for point compression (elliptic curves for example are not rational). It the above example you could send b and one bit indicatig whether we use the biggest or the smallest number among a or p-a where a is a square root of 1 db^2 in F. A similar trivial idea in the case of ECC has been patented by certicom.</p> <p>Michel</p> Perhaps you should point out that DH key exchange makes sense in ANY group for which the discrete logarithm problem is hard. One popular choice is the group of rational points on an elliptic curve (ECC). Another possible choice is apparently the group of rational points on a torus.

Of course there are no groups for which the DL problem has been PROVED to be hard.

Rationality is not really necessary for point compression (elliptic curves for example are not rational). It the above example you could send b and one bit indicatig whether we use the biggest or the smallest number among a or p-a where a is a square root of 1 db^2 in F. A similar trivial idea in the case of ECC has been patented by certicom.

Michel

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