Abstract: A new trapdoor one-way function is provided. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points.

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 method of generating a public key in a secure digital communication system, having at least one trusted entity CA and subscriber entities A. The trusted entity selects a unique identity distinguishing each entity A. The trusted entity then generates a public key reconstruction public data of the entity A by mathematically combining public values obtained from respective private values of the trusted entity and the entity A. The unique identity and public key reconstruction public data of the entity A serve as A's implicit certificate. The trusted entity combines the implicit certificate information with a mathematical function to derive an entity information f and generates a value kA by binding f with private values of the trusted entity. The trusted entity transmits the value kA to the entity to permit A to generate a private key from kA, A's private value and A's implicit certificate.

Abstract: A method of generating a public key in a secure digital communication system, having at least one trusted entity CA and subscriber entities A. The trusted entity selects a unique identity distinguishing each entity A. The trusted entity then generates a public key reconstruction public data of the entity A by mathematically combining public values obtained from respective private values of the trusted entity and the entity A. The unique identity and public key reconstruction public data of the entity A serve as A's implicit certificate. The trusted entity combines the implicit certificate information with a mathematical function to derive an entity information ƒ and generates a value kA by binding ƒ with private values of the trusted entity. The trusted entity transmits the value kA to the entity to permit A to generate a private key from kA, A's private value and A's implicit certificate.

Abstract: A system and method are provided for enabling a symmetric key to be derived, the method comprising: obtaining a plurality of key parts, wherein the plurality of key parts when combined equal the symmetric key; encrypting a first of the key parts using a first cryptographic algorithm to generate a first encrypted value; encrypting one or more remaining key parts of the plurality of key parts using respective cryptographic algorithms to generate one or more additional encrypted values, wherein each key part encrypted is encrypted using a different cryptographic algorithm; and providing the first encrypted value and the one or more additional encrypted values to an other entity to enable the other entity to derive the symmetric key.

Abstract: Improper re-use of a static Diffie-Hellman (DH) private key may leak information about the key. The leakage is prevented by a key derivation function (KDF), but standards do not agree on key derivation functions. The module for performing a DH private key operation must somehow support multiple different KDF standards. The present invention provides an intermediate approach that neither attempts to implement all possible KDF operations, nor provide unprotected access to the raw DH private key operation. Instead, the module performs parts of the KDF operation, as indicated by the application using the module. This saves the module from implementing the entire KDF for each KDF needed. Instead, the module implements only re-usable parts that are common to most KDFs. Furthermore, when new KDFs are required, the module may be able to support them if they built on the parts that the module has implemented.

Abstract: An authenticated RFID system is provided that uses elliptic curve cryptography (ECC) to reduce the signature size and read/write times when compared to traditional public key implementations such as RSA. Either ECDSA or ECPVS can be used to reduce the signature size and ECPVS can be used to hide a portion of the RFID tag that contains sensitive product identifying information. As a result, smaller tags can be used or multiple signatures can be written at different stages in a manufacturing or supply chain. A key management system is used to distribute the verification keys and aggregate signature schemes are also provided for adding multiple signatures to the RFID tags, for example in a supply chain.

Abstract: An improved compression scheme for compressing an ECDSA signature is provided. The scheme substitutes the integer s in a signature (r, s) by a smaller value c. The value c is derived from s and another value d, d being small enough such that c is smaller than s. The compressed signature (r, c) is verified by computing a value using r and e, e being a hash of a message m, and using this value with a value R recovered from r to derive the value d. The value s can then be recovered and the full signature then recovered and verified.

Abstract: Methods for choosing groups for a static Diffie-Hellman key agreement protocol to inhibit active attacks by an adversary are provided. In mod p groups, an even h is chosen of value approximately ( 9/16)(log2n)2, values r and n are determined using sieving and primality testing on r and n, and a value t is found to compute p=tn+1 wherein p is prime. In elliptic curve groups defined over a binary filed, a random curve is chosen, the number of points on the curve is counted and this number is checked for value of 2n wherein n is prime and n?1 meets preferred criteria. In elliptic curve groups defined over a prime field of order q, a value n=hr+1 is computed, wherein n is prime and n?1 meets preferred criteria, and a complex multiplication method is applied on n to produce a value q and an elliptic curve E defined over q and having an order n.

Abstract: An authenticated RFID system is provided that uses elliptic curve cryptography (ECC) to reduce the signature size and read/write times when compared to traditional public key implementations such as RSA. Either ECDSA or ECPVS can be used to reduce the signature size and ECPVS can be used to hide a portion of the RFID tag that contains sensitive product identifying information. As a result, smaller tags can be used or multiple signatures can be written at different stages in a manufacturing or supply chain. A key management system is used to distribute the verification keys and aggregate signature schemes are also provided for adding multiple signatures to the RFID tags, for example in a supply chain.

Abstract: Undesirable electronic messages, such as the unsolicited broadcast e-mail known as spam, is not only a nuisance, but wastes both computer and user resources. Conversely, desirable electronic messages with sensitive content is important to secure, so that it is not forged, tampered or revealed. Accordingly, the present invention provides cryptographic methods that simultaneously secures electronic communication and helps fight spam.

Abstract: A computer implemented method of compressing a digitally represented cryptographic value. The method comprising the steps of: (a) selecting a secret value; (b) performing a cryptographic operation on the secret value to generate the cryptographic value; (c) determining whether the cryptographic value satisfies the pre-determined criteria; and (d) repeating the sequence of steps starting at step (a) until the cryptographic value satisfies the pre-determined criteria.

Abstract: Improper re-use of a static Diffie-Hellman (DH) private key may leak information about the key. The leakage is prevented by a key derivation function (KDF), but standards do not agree on key derivation functions. The module for performing a DH private key operation must somehow support multiple different KDF standards. The present invention provides an intermediate approach that neither attempts to implement all possible KDF operations, nor provide unprotected access to the raw DH private key operation. Instead, the module performs parts of the KDF operation, as indicated by the application using the module. This saves the module from implementing the entire KDF for each KDF needed. Instead, the module implements only re-usable parts that are common to most KDFs. Furthermore, when new KDFs are required, the module may be able to support them if they built on the parts that the module has implemented.

Abstract: There is provided a method of one member of a first entity generating an intra-entity public key. The first entity has a plurality of members and the one member has a long-term private key and a corresponding long-term public key. The method includes generating a short-term private key and a corresponding short-term public key, computing an intra-entity shared key by mathematically combining the short-term public key of the one member and respective short-term public keys of each other member of the first entity and computing the intra-entity public key by mathematically combining the short-term private key, the long-term private key and the intra-entity shared key.

Abstract: A method of certifying a correspondent in a data communication system by a certifying authority. The certifying authority includes a cryptographic unit. The method includes generating a random number and implicit certificate components based on the random number using the cryptographic unit. The implicit certificate components have a first component and a second component. The method also includes providing the implicit certificate components for use in the data communication system and providing a public key of the certifying authority for use in derivation of a public key of the correspondent from the first component. The certifying authority recertifies the correspondent by providing implicit certificate components using a changed value for the random number.

Abstract: A method and system are provided for authenticating and securing an embedded device using a secure boot procedure and a full non-volatile memory encryption process that implements Elliptic Curve Pinstov-Vanstone Signature (ECPV) scheme with message recovery on a personalized BIOS and master boot record. The signature includes code that is recovered in order to unlock a key that is in turn used to decrypt the non-volatile memory. The use of ECPVS provides an implicit verification that the hardware is bound to the BIOS since the encrypted memory is useless unless properly decrypted with the proper key.

Abstract: The invention relates to a method of generating an implicit certificate and a method of generating a private key from a public key. The method involves a method generating an implicit certificate in three phases. The public key may be an entity's identity or derived from an entity's identify. Only the owner of the public key possesses complete information to generate the corresponding private key. No authority is required to nor able to generate an entity's private key.

Abstract: A cryptosystem prevents replay attacks within existing authentication protocols, susceptible to such attacks but containing a random component, without requiring modification to said protocols. The entity charged with authentication maintains a list of previously used bit patterns, extracted from a portion of the authentication message connected to the random component. If the bit pattern has been seen before, the message is rejected; if the bit pattern has not been seen before, the bit pattern is added to the stored list and the message is accepted.

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 so 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: A method for communicating information between at least a pair of correspondents, the method comprising the steps of each of the correspondents selecting a plurality of cryptographic algorithms known to each of the correspondents. One of the correspondents applies the algorithms in a predetermined manner to a message for producing a set of processed information. The set of processed information is transmitted to the other correspondent. The other correspondent applies complimentary operations of the cryptographic schemes in accordance with the predetermined manner for deriving information related to the message from the processed information.