Cryptographic systems and methods are provided in which authentication operations, digital signature operations, and encryption operations may be performed. Authentication operations may be performed using authentication information. The authentication information may be constructed using a symmetric authentication key or a public/private pair of authentication keys. Users may digitally sign data using private signing keys. Corresponding public signing keys may be used to verify user signatures. Identity-based-encryption (IBE) arrangements may be used for encrypting messages using the identity of a recipient. IBE-encrypted messages may be decrypted using appropriate IBE private keys. A smart card, universal serial bus key, or other security device having a tamper-proof enclosure may use the authentication information to obtain secret key information. Information such as IBE private key information, private signature key information, and authentication information may be stored in the tamper-proof enclosure.