Questions about Shamir secret sharing

I've written a conceptual overview of a particular form of Shamir's
polynomial scheme from "How to Share a Secret", but I have some
questions regarding which liberties I can take and still get away with
it. I've copied the introduction here; the full document is at
http://halfgeek.org/ss10001/ss10001.html . If I've made any incorrect
assumptions, or if you have any answers to my questions, please reply.

Thanks a zillion -- PSM

The intro:

ss10001 is an experiment in implementing secret sharing as proposed by
Shamir[SHAMIR] by using 16-bit blocks of the secret to be shared and
evaluating polynomials modulo 65537. The goal is to provide a
speed-efficient (and hopefully, at some point, memory-efficient)
implementation of the sharing scheme while providing a level of
theoretical security at or near the number of bits of the secret
itself.

This version of the document is a request for commentary by those
better
versed in cryptanalysis than I am, having ever had only two classes on
the topic and no graduate study. I think I may be onto something
useful,
but I would not be so presumptuous as to consider it secure without
first having it reviewed by expert eyes. I have written an encrypter
and
a decrypter for this scheme, both in C, but have not released either.
The decrypter is suitable for solving shares generated from any of the
modes described below; the encrypter is currently designed to run in OC
mode. My intuition about the Shamir algorithm is not sufficient to tell
me whether OC mode provides sufficient security, or whether the more
conservative AC or the less intensive SR modes should be used instead.

This is not (yet) intended to be a formal paper; I'm really just trying
to ask some questions.

.

Relevant Pages

  • Re: Efficient Exponentiation of a Shared Secret
    ... shared among a number of parties. ... Shamir's scheme this is the case). ... Is there a scheme in which the secret s can be expressed as a product ... using any k out of n shares the secret x can be reconstructed, ...
    (sci.crypt)
  • Re: A new public key algorithm based on avalanche properties
    ... I do not understand how the OP's scheme cant work. ... (addition by a secret integer modulo a public number). ... - Has the various commutive properties that the protocol needs for this to ... Is computationally easier to compute than known believed-secure DH groups ...
    (sci.crypt)
  • Re: Joint encryption?
    ... > Google for secret sharing or secret splitting. ... Looking at Shamir's scheme, I'm surprised I didn't come up with this ... I've been reading up on secret sharing since I posted this ...
    (Bugtraq)
  • Re: k-deterministic public-private key generation
    ... Frykholm & Juels scheme looks essentially like this: ... the secret to encrypt, ... number generator for key generation, ... Guessing ...
    (sci.crypt)
  • Re: Security of SHA-1 concatenation cipher?
    ... > is there anything that would cause this scheme to be less secure than might ... If the source of data doesn't have a secret that the attacker doesn't ... verifier also knows the secret) or digital signature (if the data source ...
    (sci.crypt)