The digital revolution, fired by the development of the information and communication technologies, has fundamentally changed the way we think, behave, communicate, work and earn livelihood (the World Summit on the Information Society). These technologies have affected all aspects of our society and economy. However, the Information Society developments present us not only with new benefits and opportunities, but also with new challenges. Information security is one of these challenges, and nowadays, information security mechanisms are inevitable components of virtually every information system. Information authentication is one of the basic information security goals, and it addresses the issues of source corroboration and improper or unauthorized modification of data. More specific, data integrity is the property that the data has not been changed in an unauthorized manner since its creation, transmission or storage. Data origin authentication, or message authentication, is the property whereby a party can be corroborated as a source of the data. Usually, message authentication is achieved by appending an authentication tag or a digital signature to the message. The authentication tag (resp., digital signature) is computed in such a way so that only an entity that is in possession of the secret key can produce it, and it is used by the verifier to determine the authenticity of the message. During this procedure, the message is considered to be an atomic object in the following sense. The verifier needs the complete message in order to check its validity. Presented with the authentication tag (resp., digital signature) and an incomplete message, the verifier cannot determine whether the presented incomplete message is authentic or not. We consider a more general authentication model, where the verifier is able to check the validity of incomplete messages. In particular, we analyze the cases of erasure-tolerant information authentication and stream authentication.