In the Shamir secret sharing scheme, we distribute a secret among q different users asfollows. If our secret a message (m₁, ..., mk) from V(k, q) then, we encode it as acodeword of the Reed-Solomon RS (9) and give one coordinate to each user. In thisproblem, we will use q = 7, k = 4 and the parity check matrix H₁ below for RS4(7).HA=11011 11 12 3 4 5 64224 11. Write a generator matrix for RS4 (7) of the form Hq-k.

To construct a Reed-Solomon code , we need to determine its parity-check matrix .Here we have to…

Answered: In the Shamir secret sharing scheme, we…

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

See similar textbooks

Similar questions

Write out the addition and multiplication tables for 4.
We would like to design a linear block code (2,6) using the generator matrix: [100110] G=010111 o01101 What is the codework sequence (i.e. output of the channel encodder) for the data sequence (i.e. input of the channel encoder) 011000101111?
Find the standard generator matrix for a (4, 2) linear code over Z3that encodes 20 as 2012 and 11 as 1100. Determine the entire codeand the parity-check matrix for the code. Will the code correct allsingle errors?
Why can’t the nearest-neighbor method with a (4, 2) binary linearcode correct all single errors?
7. Use the algorithm introduced in section 2.2 to find the inverse, if it exists, of the following matrix. -2 -3 1 -3 1 -4 1 -3 -2
Describe the family of shift ciphers as a cryptosytem.
Five jobs are to be assigned to 5 machines to minimize the total time required to process the jobs on machines. The times in hours for processing each job on each machine are given in the matrix below. By using assignment algorithm make the assignment for minimizing the time of processing. Jobs U V W X Y A 2 4 3 5 4 B 7 4 6 8 4 C 2 9 8 10 4 D 8 6 12 7 4 E 2 8 5 8 8
(13) Find two different complete systems of residues modulo 8.
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.
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 RS(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). HA = 1 1 1 1 1 1 1 1 2 3 4 5 6 0 1 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.
To measure the work completed by an algorithm, we often count flops, the number of floating-point additions subtractions, multiplications, or divisions. Let a be a real number, m, n, and r be positive integers, u, v, and x be n-dimensional column vectors, y be an m-dimensional column vector, A be an m x r matrix, B be an r x n matrix, and C' be an m x n matrix. Give the number of flops required for each of the following calculations. a. The dot product of vectors u and v b. y + Cx c. C+YxT d. C + AB
Use A−1 to decode the cryptogram.

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS