[Cryptography] Shamir’s secret sharing

[Phillip Hallam-Baker]

On Wed, Jun 19, 2019 at 8:50 PM Adrian McCullagh <
amccullagh at odmoblawyers.com> wrote:

> Can anyone point me to any papers dealing with the issue of whether
> Shamir’s Secret Sharing scheme is quantum crypto resistant.  In particular
> if it is resistant does the resistance improve if the complexity of the
> scheme increases.  That is, with n out of t, is 2 out of 3 keys less
> resistant that say 11 out of 21?
>
>
>
> Kind Regards
>
>
>
> Adrian
>
> Dr. Adrian McCullagh
>
> Ph.D. (IT Sec) LL.B.(Hons) B. App. Sc. (Computing)
> *ODMOB* *Lawyers*
>
> *Research* *Fellow*: *Law* *Futures* *Centre*
>
> Griffith University
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> Mobile +61 (0) 401 646 486
>

It doesn't matter how much compute power you have. Unless there is some
weakness in the choice of the shares, Shamir Secret Sharing is provably
secure because if you have a quorum of n shares, you have a polynomial of
degree n-1.

It takes two points to define a line, three a quadratic curve, etc. etc.
There simply isn't enough information to reconstruct the polynomial unless
you have sufficient shares.

>
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