the full version of the extended abstract which appears in Africacrypt ’10 (3 – 6 may 2010, Stellenbosch, South Africa) D. Bernstein and T. Lange Eds., Springer-Verlag, LNCS 6055, pages 297–315. Strong Cryptography from Weak Secrets Building Efficient PKE and IBE from Distributed Passwords Xavier Boyen1, Céline Chevalier2, Georg Fuchsbauer3, and David Pointcheval3 1 Université de Liège, Belgium 2 Telecom ParisTech, Paris, France 3 École Normale Supérieure, CNRS-INRIA, Paris, France Distributed-password public-key cryptography (DPwPKC) allows the members of a group of people, each one holding a small secret password only, to help a leader to perform the private operation, associated to a public-key cryptosystem. Abdalla et al. recently defined this tool [1], with a practical construction. Unfortunately, the latter applied to the ElGamal decryption only, and relied on the DDH assumption, excluding any recent pairing-based cryptosystems. In this paper, we extend their techniqu...