Laboratoire IMATH

Titre :
Efficient succinct zero-knowledge arguments in the CL framework

Résumé :
The CL encryption scheme, introduced by Castagnos and Laguillaumie in 2015, is an efficient linearly homomorphic public key encryption scheme, based on class groups of imaginary quadratic fields. The specificity of these groups is that their order is hard to compute, which means it can be considered as unknown. This particularity, while being key in the security of the scheme, brings a few technical challenges in working with CL, especially in the design of zero-knowledge protocols.

To solve these difficulties, a closer look at CL ciphertexts reveals the necessity of a new notion of soundness that we call soundness with partial extractability. Thanks to this notion, we design efficient zero-knowledge proofs and arguments for different CL statements, such as a batch proof of correctness, or an argument for a multiexponentiation.

Joint work with G. Castagnos and F. Laguillaumie.