It seems that randomised encoding, as you are probably already aware, allows for two functions f(x)
and g(x, r)
that satisfy the following two properties.
- Correctness: there exists some function
D
such thatf(x) = D(g(x, r))
. - Privacy: knowledge of
g(x, r)
will not feasibly reveal any knowledge off(x)
to differentiate it fromf(y)
without comparingg(x, r)
andg(y, r)
.
On the other hand indistinguishability obfuscation allows a function f(x)
that satisfies the following two properties.
- Completeness: there exists some function
DE
such thatf(x) = DE(x)
. - Indistinguishability: knowledge of
DE(x)
will not feasibly reveal any knowledge off(x)
to differentiate it fromf(y)
without comparingDE(x)
andDE(y)
.
If DE(x) = g(x, r) = D(g(x, r))
was true, and the properties were otherwise satisfied, then completeness and indistinguishability would be satisfied as equivalent to correctness and privacy. Hence, in this case randomised encryption would be equivalent to indistinguishability obfuscation. However, randomised encryption expands further on this to say that g(x, r)
could be any function, and not necessarily equal to DE(x)
.
Further reading that might be of interest for the topic can be found here and here.