Blinding is a popular and well-known countermeasure to protect public-key cryptosystems against side-channel attacks. The high level idea is to randomize an exponentiation in order to prevent multiple measurements of the same operation on different data, as such measurements might allow the adversary to learn the secret exponent. Several variants of blinding have been proposed in the literature, using additive or multiplicative secret-sharing to blind either the base or the exponent. These countermeasures usually aim at preventing particular side-channel attacks (mostly power analysis) and come without any formal security guarantee.
In this work we investigate to which extend blinding can provide
of side-channel attacks. Surprisingly, it turns out that in the context of public-key encryption some blinding techniques are more suited than others. In particular, we consider a
version of ElGamal public-key encryption where
that the scheme, instantiated over bilinear groups of prime order
− − 1 is not smooth) is leakage resilient in the generic-group model. Here we consider the model of
in the presence of
, i.e., the scheme remains chosen-ciphertext secure even if with
decryption query the adversary can learn a bounded amount (roughly log(
)/2 bits) of arbitrary, adversarially chosen information about the computation.
that the scheme, instantiated over arbitrary groups of prime order
− − 1 is not smooth) is leakage resilient.
Previous to this work no encryption scheme secure against continuous leakage was known. Constructing a scheme that can be
secure in the
remains an interesting open problem.