Abstract: The public key, either short term “session” key or long term key, is generated by combining a pair of components. A first component is obtained by utilizing an integer with a relatively low Hamming weight as an exponent to facilitate exponentiation. The second component is a precomputed secret value that is of the form resulting from the exponentiation of the generator of the group element by an integer that has the requisite Hamming weight. The two components are combined to provide the public key and the two exponents combined to provide the corresponding private key.

Abstract: A method and apparatus for authenticating a pair of correspondents C,S in an information exchange session to permit exchange of information therebetween. The first correspondent C having log on applets and the correspondent having means for processing applets.

Abstract: A public key encryption system exchanges information between a pair of correspondents. The recipient performs computations on the received data to recover the transmitted data or verify the identity of the sender. The data transferred includes supplementary information that relates to intermediate steps in the computations performed by the recipient.

Abstract: A key establishment protocol includes the generation of a value of cryptographic function, typically a hash, of a session key and public information. This value is transferred between correspondents together with the information necessary to generate the session key. Provided the session key has not been compromised, the value of the cryptographic function will be the same at each of the correspondents. The value of the cryptographic function cannot be compromised or modified without access to the session key.

Abstract: The present invention relates to digital signature operations using public key schemes in a secure communications system and in particular for use with processors having limited computing power such as ‘smart cards’. This invention describes a method for creating and authenticating a digital signature comprising the steps of selecting a first session parameter k and generating a first short term public key derived from the session parameter k, computing a first signature component r derived from a first mathematical function using the short term public key, selecting a second session parameter t and computing a second signature component s derived from a second mathematical function using the second session parameter t and without using an inverse operation, computing a third signature component using the first and second session parameters and sending the signature components (s, r, c) as a masked digital signature to a receiver computer system.

Abstract: The present invention relates to digital signature operations using public key schemes in a secure communications system and in particular for use with processors having limited computing power such as ‘smart cards’. This invention describes a method for creating and authenticating a digital signature comprising the steps of selecting a first session parameter k and generating a first short term public key derived from the session parameter k, computing a first signature component r derived from a first mathematical function using the short term public key, selecting a second session parameter t and computing a second signature component s derived from a second mathematical function using the second session parameter t and without using an inverse operation, computing a third signature component using the first and second session parameters and sending the signature components (s, r, c) as a masked digital signature to a receiver computer system.

Abstract: A digital signature protocol generates a signature component using a hash of an encrypted message. The component and encrypted message form a signature pair that is forwarded to a recipient. The encryption message is used to retrieve the encryption key at the recipient and authenticate information in the message. The signature pair may be applied to a data carrier as a bar code for use in mail delivery services. By utilizing a hash of the message, a reduced message length is achieved as individual signatures are not required for each component of the message.

Abstract: A method of generating a private key for use in a public key data communication system implemented between a pair of correspondents is disclosed. The method comprises the steps of generating a random number for use as a private key and testing the number against a predetermined set of criteria The criteria are chosen to determine the statistical randomness of the number. The random number is utilized as a key upon satisfying the criteria.

Abstract: A method for verifying the authenticity of messages exchanged between a pair of correspondents in an electronic conducted over a data transmission system where the correspondents each include respective signing and verifying portions of a first signature scheme and a second signature scheme different from the first and utilizing an elliptic curve cryptosystem.

Abstract: An elliptic curve encryption system represents coordinates of a point on the curve as a vector of binary digits in a normal basis representation in F.sub.2.spsb.m. A key is generated from multiple additions of one or more points in a finite field. Inverses of values are computed using a finite field multiplier and successive exponentiations. A key is represented as the coordinates of a point on the curve and key transfer may be accomplished with the transmission of only one coordinate and identifying information of the second. An encryption protocol using one of the coordinates and a further function of that coordinate is also described.

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 public and private information of respective ones of the correspondents.

Abstract: This invention discloses a method of authenticating a signature of a message m comprising the steps of determining a hash h(m) of the message by application of a hash function and deriving therefrom a first signature component. The signor then computes a function mathematically related to the hash of the message and applies the function to the message to obtain a second signature component, bound to the signatory. The signature components are forwarded to a recipient. The recipient then recovers from one of the signature components a message m' and computing a value of m' by applying the hash function, and determining if the value of m' and the hash h(m) embodied in the first signature component are identical whereby identity indicates an authentic signature of the message.

Abstract: A Galois Field arithmetic logic unit (GF ALU) circuit (200) that generates a GF product of size M includes a first and a second input field element register (205, 210), a result field element register (215), a plurality, I, of subfield sets of logic gates (255, 260, 265), a plurality, S, of extension sets of logic gates (270, 275), and 3M switches (135). M is equal to S multiplied by I. A Galois Field of size M, S, and I each has an optimal normal basis. The first and second input field element registers (205, 210) are alternately coupled to the result field element register (215) by the I subfield sets of logic gates (255, 260, 265) in a first configuration and by the S extension sets of logic gates (270, 275) in a second configuration. The 3M switches (135) alternate the first and second configurations.

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 protocol appropriate for use with smartcard purchase applications such as those that might be completed between a terminal or ATM and a users personal card. The protocol provides a signature scheme which allows the card to authenticate the terminal without unnecessary signature verification which is an computationally intense operation for the smart card. The only signature verification required is that of the terminal identification (as signed by the certifying authority, or CA, which is essential to any such protocol). In the preferred embodiment, the protocol provides the card and terminal from fraudulent attacks from impostor devices, either a card or terminal.

Abstract: A cryptosystem utilizes the properties of discrete logs in finite groups, either in a public key message exchange or in a key exchange and generation protocol. If the group selected has subgroups of relatively small order, the message may be exponentiated by a factor of the order of the group to place the message in a subgroup of relatively small order. To inhibit such substitution, the base or generator of the cryptosystem is chosen to be a generator of a subgroup of prime order or a subgroup of an order having a number of relatively small divisors. The message may be exponentiated to each of the relatively small divisors and the result checked for the group identity. If the group identity is found, it indicates a vulnerability to substitution and is rejected.

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 public and private information of respective ones of the correspondents.

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 public and private information of respective ones of the correspondents.

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 public and private information of respective ones of the correspondents.

Abstract: A multiplier for obtaining the product of two elements in the field GF(2.sup.m) utilises the normal basis representation of each element. The product is also represented in normal basis form with each binary digit of the bit vector being determined by a sum of the product of the binary digits representing the two elements. By grouping like ones of one of the binary digits in the expression for the binary digit of the product and offsetting the suffixes of the binary digits, it is possible to accumulate grouped terms of each of the binary digits of the product simultaneously.