Abstract: Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and that v=w/z. The verification equality R=uG+vQ may then be computed as ?zR+(uz mod n)G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.

Abstract: An elliptic curve random number generator avoids escrow keys by choosing a point Q on the elliptic curve as verifiably random. An arbitrary string is chosen and a hash of that string computed. The hash is then converted to a field element of the desired field, the field element regarded as the x-coordinate of a point Q on the elliptic curve and the x-coordinate is tested for validity on the desired elliptic curve. If valid, the x-coordinate is decompressed to the point Q, wherein the choice of which is the two points is also derived from the hash value. Intentional use of escrow keys can provide for back up functionality. The relationship between P and Q is used as an escrow key and stored by for a security domain. The administrator logs the output of the generator to reconstruct the random number with the escrow key.

Abstract: A method of communicating in a secure communication system, comprises the steps of assembling a message at a sender, then determining a frame type, and including an indication of the frame type in a header of the message. The message is then sent to a recipient and the frame type used to perform a policy check.

Abstract: Methods, systems, and computer programs for performing key agreement operations in a communication system are described. In some aspects, a wireless network operator receives a mobile device identifier and accesses a secret key associated with the mobile device. A message authentication code function is evaluated based on the secret key to produce an output value. A session key and a challenge value are obtained based on the output value. In some aspects, a mobile device accesses a secret key in response to receiving the challenge value from the wireless network operator. A message authentication code function is evaluated based on the secret key to produce an output value. A response value and a session key are obtained based on the output value. The response value is transmitted to the wireless network operator.

Abstract: A method of transmitting messages from a sender to a recipient over a wireless channel, the messages including a sequence counter and a frame counter. The method comprises establishing initial values of the sequence counter and the frame counter at the sender. Initial values of the frame counter and the sequence counter are provided to the recipient. The sender sends compressed messages including the value of the sequence counter and not the frame counter and monitors for an acknowledgement of receipt by the recipient. When no acknowledgment is received, the sender sends uncompressed messages until an acknowledgement of receipt is received from the recipient. The sequence counter is incremented and the next value of the frame counter is established as the integer next larger than previous value of the frame counter which is congruent to the sequence counter modulo 256.

Abstract: Methods, systems, and computer programs for using an implicit certificate are described. In some aspects, an implicit certificate is accessed. The implicit certificate is associated with an entity and generated by a certificate authority. The implicit certificate includes a public key reconstruction value of the entity. Certificate authority public key information is accessed. The certificate authority public key information is associated with the certificate authority that issued the implicit certificate. A first value is generated based on evaluating a hash function. The hash function is evaluated based on the certificate authority public key information and the public key reconstruction value of the entity. A public key value of the entity can be generated or otherwise used based on the first value.

Abstract: A method for providing Cheon-resistance security for a static elliptic curve Diffie-Hellman cryptosystem (ECDH), the method including providing a system for message communication between a pair of correspondents, a message being exchanged in accordance with ECDH instructions executable on computer processors of the respective correspondents, the ECDH instructions using a curve selected from a plurality of curves, the selecting including choosing a range of curves; selecting, from the range of curves, curves matching a threshold efficiency; excluding, within the selected curves, curves which may include intentional vulnerabilities; and electing, from non-excluded selected curves, a curve with Cheon resistance, the electing comprising a curve from an additive group of order q, wherein q is prime, such that q?1=cr and q+1=ds, where r and s are primes and c and d are integer Cheon cofactors of the group, such that cd?48.

Abstract: Methods, systems, and computer programs for using an implicit certificate are disclosed. In some aspects, a message and an implicit certificate are accessed. The implicit certificate is associated with an entity. A modified message is generated by combining the message with a value based on the implicit certificate. A digital signature can be generated based on the modified message and transmitted to a recipient. In some aspects, a digital signature from an entity and a message to be verified based on the digital signature are accessed. An implicit certificate associated with the entity is accessed. A modified message is generated by combining the message with a value based on the implicit certificate. The message is verified based on the digital signature and the modified message.

Abstract: A serialization service module is provided for configuring an asset management system to provide a secure means of generating, assigning to chips (or other electronic objects or devices), and tracking unique serial numbers. To provide this service, a controller connects through a secure, encrypted connection to appliances at a manufacturer's location. Agents can then request serial number values from an appliance by product name. The serial numbers are generated by the appliance, metered, and provided to the agents. The serial numbers are then injected sequentially into each die in a chip manufacturing process using the agent. A log is reported to the controller.

Abstract: A method of communicating in a secure communication system, comprises the steps of assembling a message at a sender, then determining a frame type, and including an indication of the frame type in a header of the message. The message is then sent to a recipient and the frame type used to perform a policy check.

Abstract: Methods, systems, and computer programs for generating cryptographic function parameters are described. In some examples, a solution to a puzzle is obtained. A pseudorandom generator is seeded based on the solution. After seeding the pseudorandom generator, an output from the pseudorandom generator is obtained. A parameter for a cryptographic function is generated. The parameter is generated from the output from the pseudorandom generator.

Abstract: Systems, methods, software, and combinations thereof for evaluating entropy in a cryptography system are described. In some aspects, sample values are produced by an entropy source system. A typicality can be determined for each of the sample values. A grading is determined for preselected distributions based on the typicalities of the sample values. A subset of the preselected distributions are selected based on the gradings. An entropy of the entropy source system is calculated based on the subset of the plurality of distributions.

Abstract: Systems, methods, and software can be used to generate elliptic curve points. In some aspect, the method includes: selecting a field size of 8?91+5; selecting a curve equation that is compatible to the field size; using, by a hardware processor, the selected field size to generate an elliptic curve point; and using, by the hardware processor, the elliptic curve point in an Elliptic Curve Cryptography (ECC) operation.

Abstract: A method of transmitting messages from a sender to a recipient over a wireless channel, the messages including a sequence counter and a frame counter. The method comprises establishing initial values of the sequence counter and the frame counter at the sender. Initial values of the frame counter and the sequence counter are provided to the recipient. The sender sends compressed messages including the value of the sequence counter and not the frame counter and monitors for an acknowledgement of receipt by the recipient. When no acknowledgment is received, the sender sends uncompressed messages until an acknowledgement of receipt is received from the recipient. The sequence counter is incremented and the next value of the frame counter is established as the integer next larger than previous value of the frame counter which is congruent to the sequence counter modulo 256.

Abstract: Methods, systems, and computer programs for performing key agreement operations in a communication system are described. In some aspects, a wireless network operator receives a mobile device identifier and accesses a secret key associated with the mobile device. A message authentication code function is evaluated based on the secret key to produce an output value. A session key and a challenge value are obtained based on the output value. In some aspects, a mobile device accesses a secret key in response to receiving the challenge value from the wireless network operator. A message authentication code function is evaluated based on the secret key to produce an output value. A response value and a session key are obtained based on the output value. The response value is transmitted to the wireless network operator.

Abstract: Trust between entities participating in an upgrade or enablement/disablement process is established and, to facilitate this remotely and securely, a highly tamper resistant point of trust in the system that is being produced is used. This point of trust enables a more efficient distribution system to be used. Through either a provisioning process or at later stages, i.e. subsequent to installation, manufacture, assembly, sale, etc.; the point of trust embodied as a feature controller on the device or system being modified is given a feature set (or updated feature set) that, when validated, is used to enable or disable entire features or to activate portions of the feature.

Abstract: A method of verifying a pair of correspondents in electronic transaction, the correspondents each including first and second signature schemes and wherein the first signature scheme is computationally more difficult in signing than verifying and the second signature scheme is computationally more difficult in verifying than signing. The method comprises the step of the first correspondent signing information according to the first signature scheme and transmitting the first signature to the second correspondent, the second correspondent verifying the first signature received from the first correspondent, wherein the verification is performed according to the first signature scheme.

Abstract: The invention provides a method of verifiable generation of public keys. According to the method, a self-signed signature is first generated and then used as input to the generation of a pair of private and public keys. Verification of the signature proves that the keys are generated from a key generation process utilizing the signature. A certification authority can validate and verify a public key generated from a verifiable key generation process.

Abstract: There is provided a method for secure communications. The method includes a computing device receiving a notification comprising a message, a counter value, a signature signed by a signer and based on the message and the counter value, and an indication of the signer. The device obtains a current counter value based on an identity of the signer, checks the signature and compares the counter value with the current counter value; and, if the counter comparison and the signature checking is successful, accepting the message.

Abstract: Systems, methods, and software can be used to provide security assurance information. In some aspects, a certificate request for a client process on a mobile device is received. A security assurance character for the client process is determined. Whether to grant the certificate request is determined based on the determined security assurance character. In response to determining to grant the certificate request, a certificate is generated.