signer, and handles the adding of users to and the removal of users from the group—usually by issuing or revoking group membership certificates. The anonymity, unlinkability, and anonymity revocation provided by group signatures lends itself for a variety of privacy sensitive applications like voting, bidding, anonymous payment, and anonymous credentials An efficient constructions for group signatures was given by Ateniese, Camenisch, Joye, and Tsudik. The most efficient multi-show unlinkable anonymous credential systems—the latter is essentially a low profile version of idemix—are based on similar ideas. This is particularly true for credential systems that provide efficient means for implementing anonymous multi-show credentials with credential revocation. Both schemes are based on techniques for doing proofs of knowledge. Proofs of knowledge relying on the discrete logarithm problem for groups of known order and on the special RSA problem for groups of hidden order form the basis for most of today's group signature and anonymous credential systems. Moreover, direct anonymous attestation a protocol for authenticating trusted platform modules is based on the same techniques. Direct anonymous attestation can be seen as the first commercial application of multi show anonymous digital credentials, even though in this case credentials are not attached to persons, but to chips and consequently computer platforms. From an applications' point of view, the main advantage of Camenisch et al.'s multi-show unlinkable credentials over the more efficient Brands credentials is the multi-show unlinkable property. However, this property is mainly of practical interest in an off-line setting. Brands credentials provide a mechanism that gives analogous functionality without sacrificing performance: an efficient batch issuing protocol which can simultaneously issue many unlinkable credentials. This mechanism can be combined with a privacy preserving certificate refresh process (which gives a fresh unlinkable credential with the same attributes as a previous spent credential). Online credentials for learning Online credentials for learning are digital credentials that are offered in place of traditional paper credentials for a skill or educational achievement. Directly linked to the accelerated development of internet communication technologies, the development of digital badges, electronic passports and massive open online courses (MOOCs) have a very direct bearing on our understanding of learning, recognition and levels as they pose a direct challenge to the status quo. It is useful to distinguish between three forms of online credentials: Test-based credentials, online badges, and online certificates. See also Sources References Cryptographic protocols