Logical Relations for Encryption

Logical Relation for Encryption
(new!)
The relation environment ϕ gives the relation ϕ(k)
between values encrypted by each secret key k
ϕ{v 1 } k1 ∼ {v 2 } k2 : bits[τ]⇔
(v 1 , v 2 ) ∈ ϕ(k)where k = k1 = k2
ϕnew k in e 1 ∼ new k in e 2 : τ⇔
ϕ, k a re 1 ∼ e 2 : τ for some r
E.g., new k in 〈{1} k , λ{x} k . x mod 2〉
and new k in 〈{3} k , λ{x} k . x mod 2〉
can be related by taking k a {(1,3)}