VE475 Introduction to Cryptography Assignment 9 solved

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Ex. 1 — Missile or not missile. . .
In a military office one general, two colonels, and five desk clerks control a powerful missile. As nobody
wants the missile to be launched by mistake the following rules are set.
ˆ The general can decide to launch to missile.
ˆ Two colonels can decide to launch to missile.
ˆ Five desk clerics can decide to launch to missile.
ˆ One colonel and three desk clerks can decide to launch to missile.
Describe how a secret sharing scheme can be used to solve this problem.
Ex. 2 — Asmuth-Bloom Threshold Secret Sharing Scheme
Explain how to take advantage of the Chinese remainder Theorem in order to build a Threshold Secret
Sharing Scheme.
Ex. 3 — Shamir’s Threshold Secret Sharing Scheme
In the lecture it was presented how to recover the shared secret using the Vandermonde matrix. Explain
how this can also be done using the Lagrange’s interpolation method. Solve the lecture’s example using
the new approach.
Ex. 4 — Simple questions
1. In a Blakley scheme, suppose Alice and Bob are given the planes z = 2x + 3y + 13 and z =
5x + 3y + 1. Show that they can recover the secret without the help of Charly.
2. Prove that the determinant of the Vandermonde matrix V of order n is det V =
(xk −xj ).
3. Complete the IDEA survey for VE475 and get 5 bonus marks on the assignments.
Ex. 5 — Reed Solomon codes
1. Describe the Reed Solomon code C.
2. Reusing the same notations as in the lecture and the distance of the Reed-Solomon code, give
some condition on k such that for any coalition of size 2, it is possible to identify a parent of a
descendant of C.