Event: subset of outcomes from a probability space
Head = { H }
Valid = { H, T }
P(A) = ΣweA P(w)
1 – P(E) = P(Valid)
Complementary Event Prbability
VA: P(a) + p(A) = 1
Conditional probability
P(B|A) = P(Aub)/ p(A)
Perfect Cipher
the ciphertext provides an attacker with no additional information about the plaintext.
m -> enc -> c
m e M
m* e M
Eki(mi) = c
P(m=m*).P(k=k*) = 1/k
P(Ek(m)= c) = 1/|k|
P(m=m* Ek(m)=c) = P(m = m*)/|k|
Malleable
alice Ek(m)=c active attacker
Impratical |k| = |m|
Shamon’s Theorem: if a cipher is perfect, it must be impractical
Perfect cipher: P(m=m*|Ek(m)=c) = P(m=m*)
