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Leakage-resilient Algebraic Manipulation Detection Codes with Optimal Parameters
Algebraic Manipulation Detection (AMD) codes [CDF+08] are keyless message
authentication codes that protect messages against additive tampering by the
adversary assuming that the adversary cannot see the codeword. For certain
applications, it is unreasonable to assume that the adversary computes the
added offset without any knowledge of the codeword c. Recently, Ahmadi and
Safavi-Naini [AS13], and then Lin, Safavi-Naini, and Wang [LSW16] gave a construction
of leakage-resilient AMD codes where the adversary has some partial
information about the codeword before choosing added offset, and the scheme
is secure even conditioned on this partial information.
In this paper we show the bounds on the leakage rate r and the code rate k
for leakage-resilient AMD codes. In particular we prove that 2r + k < 1 and for
the weak case (security is averaged over a uniformly random message) r + k < 1.
These bounds hold even if adversary is polynomial-time bounded, as long as we
allow leakage function to be arbitrary.
We present the constructions of AMD codes that (asymptotically) fulfill
above bounds for almost full range of parameters r and k. This shows that
above bounds and constructions are in-fact optimal.
In the last section we show that if a leakage function is computationally
bounded (we use Ideal Cipher Model) then it is possible to break these bounds