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In the Shamir secret sharing scheme, we distribute a secret among q 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 H4 below for RS4 (7). НА = 1 1 1 1 1 1 1 01 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. Explain why they can't recover the secret with only this information.

In the Shamir secret sharing scheme, we distribute a secret among q 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 H4 below for RS4 (7). НА = 1 1 1 1 1 1 1 01 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. Explain why they can't recover the secret with only this information.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In the Shamir secret sharing scheme, we distribute a secret among q 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 RS4(7). 4 HA = 1 1 1 1 1 1 1 0 1 2 3 4 5 6 14 2 2 4 1 0 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. Explain why they can't recover the secret with only this information.
Transcribed Image Text:In the Shamir secret sharing scheme, we distribute a secret among q 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 RS4(7). 4 HA = 1 1 1 1 1 1 1 0 1 2 3 4 5 6 14 2 2 4 1 0 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. Explain why they can't recover the secret with only this information.
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