Secret sharing scheme

Question 1

def of secret sharing scheme

Question 2

definition of perfect security for a secret sharing scheme

Question 3

th: size of the sharing for secret sharing scheme and proof

Question 4

th: randomness of the Split algorithm for secret sharing scheme and proof

Question 5

definition of additive secret sharing scheme

Question 6

Lemma: additive masking and proof

Question 7

th: security of additive secret sharing scheme and proof

Question 8

definition of replicated secret sharing scheme and its security

Question 9

lagrange interpolation

Question 10

definition of vandermond matrix and of its modified version

Question 11

def of vandermond interpolation

Question 12

proof of vandermond interpolation

Question 13

proof of modified vandermonde matrix

Question 14

def of shamir secret sharing scheme

Question 15

security of shamir secret sharing scheme (dim saltata)

Question 16

Exercise 1.
Prove that Shamir Secret Sharing is not perfectly secure if the
operations are performed over Z.
Consider a (3, n)-Shamir secret sharing scheme (n ≥ 3) over the integers. Prove
that knowledge of two points (1, y1) and (2, y2) reveals the parity of the secret s.