Certicom Corporation

Blackberry Corporation

Daniel Richard Brown

Neil Patrick Adams

Scott Alexander Vanstone

Robert John Lambert

Marinus Struik

Robert Philip Gallant

Ashok Vadekar

David William Kravitz

Darryl L Parisien

Matthew John Campagna

Dinah Lea Marie Davis

Gregory Marc Zaverucha

Adrian Antipa

Brian Neill

Keelan Smith

Alfred John Menezes

Tony Rosati

Anthony J Walters

Randy Tsang

Walt Davis

Michael Griffiths-Harvey

Johnathan George White

Nevine Maurice Ebeid

Robert Gallant

Christopher Labrador

Atsushi Yamada

A method for a Diffie Hellman key exchange, the method including selecting a field size p in the form p=hq+1, where q is a prime number that is one plus a factorial number b, such that q=(b!+1), and h is a cofactor, such that p=hq+1 is prime; selecting a generator integer g whose order modulo p is the prime q or is divisible by q; choosing a private key x; computing a public key gmod p by raising said generator g to the power of said private key x, using arithmetic modulo said prime field size p; sending said public key gmod p to a correspondent; receiving, from the correspondent, a second public key B comprising g raised to a second private key y selected by the correspondent, in the form g; and creating a key Bfrom the received second public key B, by raising said second public key B to the power of said private key x, using arithmetic modulo said prime field size p.

Method and system for selecting a secure prime for finite field diffie-hellman

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.

Method and apparatus for verifiable generation of public keys

A portion of the signed message in an ECPVS is kept truly confidential by dividing the message being signed into at least three parts, wherein one portion is visible, another portion is recoverable by any entity and carries the necessary redundancy for verification, and at least one additional portion is kept confidential. The additional portion is kept confidential by encrypting such portion using a key generated from information specific to that verifying entity. In this way, any entity with access to the signer's public key can verify the signature by checking for a specific characteristic, such as a certain amount of redundancy in the one recovered portion, but cannot recover the confidential portion, only the specific entity can do so. Message recovery is also provided in an elliptic curve signature using a modification of the well analyzed ECDSA signing equation instead of, e.g. the Schnorr equation used in traditional PV signature schemes.

Signatures with confidential message recovery

A method of representing crytographic values in text form is described. The text representation is formed from words selected from a vocabulary, which may include a collection of pseudowords. The text representations can be further transformed to a paragraph in an apparently grammatically correct form.

Method of providing text representation of a cryptographic value

An algorithm is provided having a matrix phase and point addition phase that permits computation of the combination of more than two point multiples. The algorithm has particular utility in elliptic curve cryptography (ECC) such as for computing scalar multiplications in, e.g. batch ECC operations, accelerating Lenstra's ECM factoring algorithm, exploiting expanded ECC certificates (which contain pre-computed multiples of a party's public key), incremental hashing based on elliptic curves, accelerating verification of ECDSA signatures, etc.

Multi-dimensional montgomery ladders for elliptic curves

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 &#x2212;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.

Accelerated verification of digital signatures and public keys

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.

Aggregate signature schemes

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.

Method and system of managing and filtering electronic messages using cryptographic techniques

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.

Method of compressing a cryptographic value

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.

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Mississauga, Canada

Daniel Richard Brown