Circular and Leakage Resilient Public-Key Encryption under Subgroup Indistinguishability
The main results of this work are new public-key encryption schemes that, under the quadratic residuosity (QR) assumption (or Paillier’s decisional composite residuosity (DCR) assumption), achieve key-dependent message security as well as high resilience to secret key leakage and high resilience to the presence of auxiliary input information.
In particular, under what we call the subgroup indistinguishability assumption, of which the QR and DCR are special cases, we can construct a scheme that has:
Key-dependent message (circular) security. Achieves security even when encrypting affine functions of its own secret key (in fact, w.r.t. affine “key-cycles” of predefined length). Our scheme also meets the requirements for extending key-dependent message security to broader classes of functions beyond affine functions using previous techniques of Brakerski et al. or Barak et al.
Leakage resiliency. Remains secure even if any adversarial low-entropy (efficiently computable) function of the secret key is given to the adversary. A proper selection of parameters allows for a “leakage rate” of (1 − o(1)) of the length of the secret key.
Auxiliary-input security. Remains secure even if any sufficiently hard to invert (efficiently computable) function of the secret key is given to the adversary.