Leakage Resilient ElGamal Encryption

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

provable security

against a

general class

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

multiplicatively blinded

version of ElGamal public-key encryption where

– we

prove

that the scheme, instantiated over bilinear groups of prime order

p

(where

p

 − − 1 is not smooth) is leakage resilient in the generic-group model. Here we consider the model of

chosen-ciphertext security

in the presence of

continuous leakage

, i.e., the scheme remains chosen-ciphertext secure even if with

every

decryption query the adversary can learn a bounded amount (roughly log(

p

)/2 bits) of arbitrary, adversarially chosen information about the computation.

– we

conjecture

that the scheme, instantiated over arbitrary groups of prime order

p

(where

p

 − − 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

proven

secure in the

standard model

remains an interesting open problem.