Abstract: A key agreement protocol for use in a public key cryptographic scheme between a pair of correspondents each of which has a long term public key and an ephemeral public key. The protocol includes the steps of exchanging the ephemeral public keys between the correspondents for computing a shared secret at each correspondent and utilizing the shared secret to obtain a common key, wherein the validity of the ephemeral public keys is checked by the recipient thereof prior to use of the common key.

Abstract: A potential bias in the generation of a private key is avoided by selecting the key and comparing it against the system parameters. If a predetermined condition is attained it is accepted. If not it is rejected and a new key is generated.

Abstract: A potential bias in the generation of a private key is avoided by selecting the key and comparing it against the system parameters. If a predetermined condition is attained it is accepted. If not it is rejected and a new key is generated.

Abstract: A digital signature scheme for a “smart” card utilizes a set of prestored signing elements and combines pairs of the elements to produce a new session pair. The combination of the elements is performed partly on the card and partly on the associated transaction device so that the exchange of information between card and device does not disclose the identity of the signing elements. The signing elements are selected in a deterministic but unpredictable manner so that each pair of elements is used once. Further signing pairs are generated by implementing the signing over an anomalous elliptic curve encryption scheme and applying a Frobenius Operator to the normal basis representation of one of the elements.

Abstract: A potential bias in the generation or a private key is avoided by selecting the key and comparing it against the system parameters. If a predetermined condition is attained it is accepted. If not it is rejected and a new key is generated.

Abstract: A digital signature scheme for a “smart” card utilizes a set of prestored signing elements and combines pairs of the elements to produce a new session pair. The combination of the elements is performed partly on the card and partly on the associated transaction device so that the exchange of information between card and device does not disclose the identity of the signing elements. The signing elements are selected in a deterministic but unpredictable manner so that each pair of elements is used once. Further signing pairs are generated by implementing the signing over an anomalous elliptic curve encryption scheme and applying a Frobenius Operator to the normal basis representation of one of the elements.

Abstract: A key agreement protocol for use in a public key cryptographic scheme between a pair of correspondents each of which has a long term public key and an ephemeral public key. The protocol includes the steps of exchanging the ephemeral public keys between the correspondents for computing a shared secret at each correspondent and utilizing the shared secret to obtain a common key, wherein the validity of the ephemeral public keys is checked by the recipient thereof prior to use of the common key.

Abstract: A key establishment protocol between a pair of correspondents includes the generation by each correspondent of respective signatures. The signatures are derived from information that is private to the correspondent and information that is public. After exchange of signatures, the integrity of exchange messages can be verified by extracting the public information contained in the signature and comparing it with information used to generate the signature. A common session key may then be generated from the pubilc and private information of respective ones of the correspondents.

Abstract: A digital signature scheme for a “smart” card utilizes a set of prestored signing elements and combines pairs of the elements to produce a new session pair. The combination of the elements is performed partly on the card and partly on the associated transaction device so that the exchange of information between card and device does not disclose the identity of the signing elements. The signing elements are selected in a deterministic but unpredictable manner so that each pair of elements is used once. Further signing pairs are generated by implementing the signing over an anomalous elliptic curve encryption scheme and applying a Frobenius Operator to the normal basis representation of one of the elements.

Abstract: A potential bias in the generation or a private key is avoided by selecting the key and comparing it against the system parameters. If a predetermined condition is attained it is accepted. If not it is rejected and a new key is generated.

Abstract: A key agreement method between a pair of entities i and j in a digital communication system, wherein each the entity has a private and corresponding public key pair Si,Pi and Sj,Pj respectively and the system, having global parameters for generating elements of a group, the method comprising the steps of: (a) entity i selecting a random private session value Ri; (b) forwarding a public session value corresponding to the private session value Ri to the entity j; (c) entity j computing a long term shared secret key k′ derived from entity i's public key and j's private key utilizing a first function H1; (d) the entity j utilizing entity j utilizing the key′ and computing an authenticated message on entity identities i,j and entities public session keys and forwarding the aunthenticated message to entity i; (e) the entity i verifying the received authenticated message; (f) the entity i computing the long term shared secret key k′ derived from the entity j's public key and i&

Abstract: A key agreement method between a pair of entities i and j in a digital data communication system, wherein each the entity has a private and corresponding public key pair Si,Pi and Sj,Pj respectively and the system, having global parameters for generating elements of a group, the method comprising the steps of: