February 2009 - cypherpunks-legacy

Fwd: Shamir secret sharing and information theoretic security
by R.A. Hettinga 24 Feb '09

24 Feb '09

Begin forwarded message: > From: hal(a)finney.org ("Hal Finney") > Date: February 23, 2009 2:30:16 PM EST > To: leichter(a)lrw.com, sbg(a)acw.com > Cc: cryptography(a)metzdowd.com, rah(a)shipwright.com > Subject: Re: Shamir secret sharing and information theoretic security > >> Is it possible that the amount of information that the knowledge of a >> sub-threshold number of Shamir fragments leaks in finite precision >> setting >> depends on the finite precision implementation? >> >> For example, if you know 2 of a 3 of 5 splitting and you also know >> that >> the finite precision setting in which the fragments will be used is >> IEEE >> 32-bit floating point or GNU bignum can you narrow down the search >> for the >> key relative to knowing no fragments and nothing about the finite >> precision implementation? > > No, not really. Think of this simple example. > > We will have two shares, x and y. Let's work mod 10 to make it > simple. The > secret value v will be x + y mod 10. The shares are created by > choosing a > random value for x, and then setting y to be v - x mod 10. > > So for example if you want to share v = 5, and x is 9, then y will > be 6: > 9 + 6 = 5 mod 10. > > Suppose that you happen to know from other information that the secret > value v is either 1 or 2. Now you learn a share value x = 5. How much > have you learned about v? > > Nothing: you can deduce that y is either 6 or 7, but you have no way > of knowing which. Whatever x had turned out to be, there would be a y > value corresponding to each possible v value. Learning a share tells > you > nothing about v, and in general Shamir sharing, learning all but one > of > the needed shares similarly tells you nothing about the secret. > > Hal Finney

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