Secret sharing scheme Flashcards

1
Q

def of secret sharing scheme

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2
Q

definition of perfect security for a secret sharing scheme

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3
Q

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

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4
Q

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

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5
Q

definition of additive secret sharing scheme

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6
Q

Lemma: additive masking and proof

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7
Q

th: security of additive secret sharing scheme and proof

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8
Q

definition of replicated secret sharing scheme and its security

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9
Q

lagrange interpolation

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10
Q

definition of vandermond matrix and of its modified version

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11
Q

def of vandermond interpolation

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12
Q

proof of vandermond interpolation

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13
Q

proof of modified vandermonde matrix

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14
Q

def of shamir secret sharing scheme

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15
Q

security of shamir secret sharing scheme (dim saltata)

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16
Q

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.