A digital signature method, a method for initializing a digital signature scheme, a system for digitally signing a message and a computer program product are described. At least the digital signature method involves a signer having a weak security parameter. The signer retrieves a cryptographic element from each of a plurality of computing entities. Each cryptographic element is a function of a commitment supplied by the signer and the commitment includes a cryptographic function of a weak security parameter provided by the signer. A strong cryptographic security parameter is generated using a plurality of said elements. A message is then signed according to the digital signature scheme using the strong cryptographic security parameter to generate a digital signature.