In the Shamir secret sharing scheme, we distribute a secret among a different users as follows. If our secret is a message (m₁, ..., mk) from V (k, q) then, we encode it as a codeword of the Reed-Solomon RSk(q) and give one coordinate to each user. In this problem, we will use q = 7, k = 4 and the parity check matrix H₁ below for RS(7). НА = 1 1 1 1 1 1 1 0 1 2 3 4 5 6 01 4 2 2 4 1 A new secret is selected and user #1 receives share value 0, user #2 receives share value 6 and user #3 receives share value 1 and are collaborating to discover the new secret. They can't recover the secret with only this information Now, suppose users #1, #2 and #3 discover, in addition to the values of their own shares, that users #4 and #5 have identical shares (but they don't necessarily know what the common value is). Using this information, first explain how they can collaborate to recover the secret and then find the secret.

In the Shamir secret sharing scheme, we distribute a secret among a different users as follows. If our secret is a message (m₁, ..., mk) from V (k, q) then, we encode it as a codeword of the Reed-Solomon RSk(q) and give one coordinate to each user. In this problem, we will use q = 7, k = 4 and the parity check matrix H₁ below for RS(7). НА = 1 1 1 1 1 1 1 0 1 2 3 4 5 6 01 4 2 2 4 1 A new secret is selected and user #1 receives share value 0, user #2 receives share value 6 and user #3 receives share value 1 and are collaborating to discover the new secret. They can't recover the secret with only this information Now, suppose users #1, #2 and #3 discover, in addition to the values of their own shares, that users #4 and #5 have identical shares (but they don't necessarily know what the common value is). Using this information, first explain how they can collaborate to recover the secret and then find the secret.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 2CEXP

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In the Shamir secret sharing scheme, we distribute a secret among q different users as follows. If our secret a message (m₁, ..., mk) from V(k, q) then, we encode it as a codeword of the Reed-Solomon RS (9) and give one coordinate to each user. In this problem, we will use q = 7, k = 4 and the parity check matrix H₁ below for RS4(7). HA = 1 1 01 1 1 1 1 2 3 4 5 6 4224 1 1. Write a generator matrix for RS4 (7) of the form Hq-k.