GENERATING IMPLICIT CERTIFICATES

Methods, systems, and computer programs for using an implicit certificate are disclosed. In some implementations, an identifier for an entity is obtained. A first cryptographic pair that includes a first private value and a first public value is generated. A second cryptographic pair that includes a second private value and a second public value is generated. Based on the first public value and the identifier for the entity, an implicit certificate IC is generated at a first computing device. Based on the implicit certificate IC, the first private value, and the second private value, a private key for the entity is generated at the first computing device. The implicit certificate IC is then sent with the second public value from the first computing device to the second computing device. The implicit certificate IC can be used, for example, to generate or verify digital signatures, to encrypt or decrypt messages, etc.