Abstract: A method for protecting a digital document and user data typed into a digital document is presented. The method comprises computation of an authentication tag when the document is sent from a server. A similar authentication tag is computed when the document is shown on a client. When another document referenced in the document is requested by the client from the server, the authentication tag computed by the client is attached to the request for that other document. The server receiving the request compares the authentication tag it computed with the one it received to verify if the request came from an authentic copy of the document. The method is suitable for protection of online banking, online investment, online shopping, and other electronic applications.

Abstract: A method for protecting a digital document and user data typed into a digital document is presented. The method comprises computation of an authentication tag when the document is sent from a server. A similar authentication tag is computed when the document is shown on a client. When another document referenced in the document is requested by the client from the server, the authentication tag computed by the client is attached to the request for that other document. The server receiving the request compares the authentication tag it computed with the one it received to verify if the request came from an authentic copy of the document. The method is suitable for protection of online banking, online investment, online shopping, and other electronic applications.

Abstract: A method for protecting a computer program against manipulation and for shielding its communication with other programs against eavesdropping and modification is presented. The method comprises the creation of individualized program copies to different groups of users, the insertion of or the derivation of individual cryptographic keys from the program code, the obfuscation of the program code, and the self-authentication of the program towards other programs. The method is suitable for the protection of online banking, online investment, online entertainment, digital rights management, and other electronic commerce applications.

Abstract: A method of performing numerical computations in a mathematical system with at least one function, including expressing the mathematical system in discrete terms, expressing at least one variable of the mathematical system as a fixed-point number, performing the computations in such a way that the computations include the at least one variable expressed as a fixed-point number, obtaining, from the computations, a resulting number, the resulting number representing at least one of at least a part of a solution to the mathematical system, and a number usable in further computations involved in the numerical solution of the mathematical system, and extracting a set of data which represents at least one of a subset of digits of the resulting number, and a subset of digits of a number derived from the resulting number.

Abstract: A method for performing computations in a mathematical system which exhibits a positive Lyapunov exponent, or exhibits chaotic behavior, comprises varying a parameter of the system. When employed in cryptography, such as, e.g., in a pseudo-random number generator of a stream-cipher algorithm, in a block-cipher system or a HASH/MAC system, unpredictability may be improved. In a similar system, a computational method comprises multiplying two numbers and manipulating at least one of the most significant bits of the number resulting from the multiplication to produce an output. A number derived from a division of two numbers may be used for deriving an output. In a system for generating a sequence of numbers, an array of counters is updated at each computational step, whereby a carry value is added to each counter. Fixed-point arithmetic may be employed. A method of determining an identification value and for concurrently encrypting and/or decrypting a set of data is disclosed.

Abstract: A method of performing numerical computations in a mathematical system with at least one function, including expressing the mathematical system in discrete terms, expressing at least one variable of the mathematical system as a fixed-point number, performing the computations in such a way that the computations include the at least one variable expressed as a fixed-point number, obtaining, from the computations, a resulting number, the resulting number representing at least one of at least a part of a solution to the mathematical system, and a number usable in further computations involved in the numerical solution of the mathematical system, and extracting a set of data which represents at least one of a subset of digits of the resulting number, and a subset of digits of a number derived from the resulting number.