Begin forwarded message: From: Sarad AV <jtrjtrjtr2...@yahoo.com> Date: February 17, 2009 9:51:09 AM EST To: cypherpu...@al-qaeda.net Subject: Shamir secret sharing and information theoretic security hi,

`I was going through the wikipedia example of shamir secret sharing`

`which says it is information theoretically secure.`

http://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing In the example in that url, they have a polynomial f(x) = 1234 + 166.x + 94.x^2 they construct 6 points from the polynomial (1,1494);(2,1942);(3,2578);(4,3402);(5,4414);(6,5615)

`the secret here is S=1234. The threshold k=3 and the number of`

`participants n=6.`

If say, first two users collude then 1494 = S + c1 .1 + c2.1 1942 = S + c1 .2 + c2.2

`clearly, one can start making inferences about the sizes of the`

`unknown co-efficients c1 and c2 and S.`

`However, it is said in the URL above that Shamir secret is information`

`theoretically secure`

in the url below they say http://en.wikipedia.org/wiki/Information_theoretic_security

`"Secret sharing schemes such as Shamir's are information theoretically`

`secure (and in fact perfectly secure) in that less than the requisite`

`number of shares of the secret provide no information about the secret."`

how can that be true? we already are able to make inferences.

`Moreover say that, we have 3 planes intersecting at a single point in`

`euclidean space, where each plane is a secret share(Blakely's scheme).`

`With 2 plane equations, we cannot find the point of intersection but`

`we can certainly narrow down to the line where the planes intersect.`

`There is information loss about the secret.`

`from this it appears that Shamir's secret sharing scheme leaks`

`information from its shares but why is it then considered information`

`theoretically secure?`

`They do appear to leak information as similar to k-threshold schemes`

`using chinese remainder theorem.`

what am i missing? Thanks, Sarad. --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to majord...@metzdowd.com