Abstract: A secure end to end connection is established between a remote device having a wireless link and a control/monitoring location for the remote device through a gateway. During the establishing of the secure connection, a compressed message representation is used to communicate between the gateway and the remote device over the wireless link and an uncompressed message representation is used to communicate between the gateway and the first location. The establishment of the secure connection utilizes public-key algorithms.

Abstract: Modular multiplication of two elements X(t) and Y(t), over GF(2), where m is a field degree, may utilize field degree to determine, at least in part, the number of iterations. An extra shift operation may be employed when the number of iterations is reduced. Modular multiplication of two elements X(t) and Y(t), over GF(2), may include a shared reduction circuit utilized during multiplication and reduction. In addition, a modular multiplication of binary polynomials X(t) and Y(t), over GF(2), may utilize the Karatsuba algorithm, e.g., by recursively splitting up a multiplication into smaller operands determined according to the Karatsuba algorithm.

Abstract: An elliptic curve processing apparatus that performs operations on elliptic curves specified over binary polynomial fields includes a functional unit that has a digit serial multiplier with a digit size of at least two bits. The elliptic curve processing apparatus performs reduction for respective generic curves using arbitrary irreducible polynomials, which correspond to respective ones of the generic curves. The elliptic curve processing apparatus may include hardwired reduction circuits in the functional unit for use with respective named curves. A storage location in the elliptic curve processing apparatus may be used to specify whether an operation is for one of the named curves or for one of the generic curves.

Abstract: Methods and systems of the present invention include providing a connection between a first computer and a second computer by receiving, at a third computer, information regarding one of the first and second computers to facilitate establishment of a secure connection between the first computer and the second computer, creating a first end-to-end security link between the first computer and third computer, and creating a second end-to-end security link between the second computer and the third computer to establish the secure connection. The first and second computers could be a client and a server on the Internet, and these methods and systems can, for example, increase the possible number of new secure connections to the server. The third computer also permits processing of information transmitted between the client and server in the third computer. For example, the information could be reformatted or used in testing a process of one of the first and second computers.

Abstract: A method and apparatus for remote access to a network server, using a secured and self-contained environment is described. In one or more embodiments of the invention, the needed software for transmission of information is readily available on portable media. The portable media can be used in conjunction with any compatible computer system to securely transfer or access information to or from Internet resources. In one or more embodiments of the invention, the operating system needed for accessing the remote server is stored on bootable media, such as a floppy disk for example. A user can reboot a computer or public terminal using the bootable media. Other portable and easily accessible media with larger memory storage capacity, such as a memory flash card, are utilized to store the necessary software for information communication.