Abstract: A method for generating an acceleration profile for a valve operating cam of an internal combustion engine varies an adjustment point of an initial draft acceleration profile curve such that a determinant of a set of equations defining valve motion constraints and scaling factors is forced to zero. The equations may then be solved for values of the scaling factors which are applied to the initial draft acceleration profile curve to generate a desired profile which satisfies valve motion constraints.

Abstract: Methods of authenticating self-authenticating documents presented at a point of purchase or financial institution. Data contained on the value document may be signed with a first digital signature and authenticated with a public key certificate. A unique personal identification number (PIN) may be included in the document data that is signed by a second digital signature. The signed data and a public key certificate are stored on the value document. At a point of purchase, a merchant or teller can scan and read the stored data and together with the PIN the customer provides, can authenticate the value document thus presented using the second digital signature. Alternatively, if the customer is not present, the document may be verified using a PIN-generating algorithm. The first digital signature alone may be used to authenticate the document even when the PIN is not available.

Abstract: System for reading a self-authenticating document having machine-readable data including critical document data, digital signature data and a public key certificate. At a point of purchase or financial institution, a personal identification unit receives a personal identification number (PIN) from a presenter of a self-authenticating document, and an image scanning and processing system reads the self-authenticating document, retrieves the machine-readable data, and assembles an authenticatable data string from the critical document data and the received PIN. A parsing system parses the machine-readable data to obtain the digital signature data and the public key certificate. A validating system certifies the public key certificate to obtain an authentic public key and applies the authentic public key to the digital signature data in order to for validate the authenticatable data string. The self-authenticating document is authenticated if the authenticatable data string is validated.