1. A computer-implemented method for validating a batch of implicit certificates, the method comprising: accessing key-pair-validation data for a batch of implicit certificates, wherein the key-pair-validation data include key-pair-validation values for each of the implicit certificates in the batch, and the key-pair-validation values for each implicit certificate are either valid or invalid according to a key-pair-validation function; and evaluating, by a computing system, a batch-validation function for the batch of implicit certificates based on the key-pair-validation data, wherein evaluating the batch-validation function identifies whether the key-pair-validation data for the batch of implicit certificates include key-pair-validation values that are invalid.