Naccache's most notable work is in public-key cryptography, including the cryptanalysis of digital signature schemes.
Together with Jacques Stern he designed the similarly named but very distinct Naccache-Stern cryptosystem and Naccache-Stern knapsack cryptosystem.
In 2004 David Naccache and Claire Whelan, then employed by Gemplus International, used image processing techniques to uncover redacted information from the declassified 6 August 2001 President's Daily Brief Bin Ladin Determined To Strike in US.
They also demonstrated how the same process could be applied to other redacted documents.Naccache is also a visiting professor and researcher at the Information Security Group of Royal Holloway, University of London.