## Section: New Results

### Hypotheses of Decisional Diffie-Hellmann

Participants : Benjamin Grégoire, Mohamad El Laz, Tamara Rezk [Inria, Indes project team] .

In the thesis work of Mohamad El Laz, co-supervised by Benjamin Grégoire and Tamara Rezk (Indes project-team), we studied the cryptographic hypothesis of DDH (Decisional Diffie-Hellman) and implementations that would break this hypothesis. We focused on ElGamal encryption cryptosystem implementations to assess they use the DDH hypothesis correctly. We analyzed a number of implementations including Botan, Belenios and Libgcrypt. The lessons learned from this analysis are that the hypotheses are not always well understood.

In a second stage we considered message encoding methods. We investigated several approaches such as DCDH (Decisional Class Diffie-Hellman) in Encoding-Free ElGamal Encryption.