Abstract: A method is disclosed whereby two parties can establish a cryptographic key for secure communications without any prior distribution of secret keys or other secret data, and without revealing said key to any third party who may have access to all of the transmissions between them. The two parties agree upon a matrix M, and two commutative families of square matrices F and G. The sender chooses a matrix S from F and a matrix T from G. The receiver independently chooses a matrix R from F and a matrix Q from G. The sender transmits the matrix SMT to the receiver and the receiver transmits the matrix RMQ to the sender. The sender computes the matrix SRMQT from the received matrix RMQ, and the receiver computes the matrix RSMTQ from the received matrix SMT. Since the matrices S and R commute, and the matrices T and Q commute, SRMQT=RSMTQ. The value of the matrix SRMTQ is then used to produce the desired cryptographic key.

Abstract: A method is disclosed whereby two parties can establish a cryptographic key for secure communications without any prior distribution of secret keys or other secret data, and without revealing said key to any third party who may have access to all of the transmissions between them. The two parties agree upon a matrix M, and independently choose matrices S and R from an established commutative family of square matrices. The sender transmits the matrix SM to the receiver and the receiver transmits the matrix RM to the sender. The sender computes the matrix SRM from the received matrix RM, and the receiver computes the matrix RSM from the received matrix SM. Since the matrices S and R commute, SRM=RSM. The value of the matrix SRM is then used to produce the desired cryptographic key. In the two-sided embodiments the two parties agree upon a matrix M, and two commutative families of square matrices F and G. The sender chooses a matrix S from F and a matrix T from G.

Abstract: One party sends a securely encrypted message to a second party. Each party chooses a secret message key for the message, which is never shared with or transmitted to any other party. The message is sent by means of three encrypted messages. The first encrypted message is sent from the sender to the receiver, and is encrypted by the sender's key. The second encrypted message is sent from the receiver back to the sender, and is encrypted by both the sender's key and then by the receiver's key. The third encrypted message is sent from the sender back to the receiver, and is encrypted by only the receiver's key following removal of the sender's key. Finally, the receiver decrypts the third message. The messages are sent in blocks. Encryption consists of multiplying each block of the message by square matrices of the same size as the block, and decryption consists of multiplying by the inverse matrices. The key matrices are taken from one or more large commutative families of matrices.

Abstract: One party sends a securely encrypted message to a second party. Each party chooses a secret message key for the message, which is never shared with or transmitted to any other party. The message is sent by means of three encrypted messages. The first encrypted message is sent from the sender to the receiver, and is encrypted by the sender's key. The second encrypted message is sent from the receiver back to the sender, and is encrypted by both the sender's key and then by the receiver's key. The third encrypted message is sent from the sender back to the receiver, and is encrypted by only the receiver's key following removal of the sender's key. Finally, the receiver decrypts the third message. The messages are sent in blocks. Encryption consists of multiplying each block of the message by a square matrix of the same size as the block, and decryption consists of multiplying by the inverse matrix. The key matrices are taken from one or more large commutative families of matrices.

Abstract: A method is disclosed whereby two parties can establish a cryptographic key for secure communications without any prior distribution of secret keys or other secret data, and without revealing said key to any third party who may have access to all of the transmissions between them. The method has both one-sided and two-sided embodiments. In the one-sided embodiments the two parties agree upon a matrix M, and independently choose matrices S and R from an established commutative family of square matrices. The sender transmits the matrix SM to the receiver and the receiver transmits the matrix RM to the sender. The sender computes the matrix SRM from the received matrix RM, and the receiver computes the matrix RSM from the received matrix SM. Since the matrices S and R commute, SRM=RSM. The value of the matrix SRM is then used to produce the desired cryptographic key. In the two-sided embodiments the two parties agree upon a matrix M, and two commutative families of square matrices F and G.

Abstract: A method is disclosed whereby two parties can establish a cryptographic key for secure communications without any prior distribution of secret keys or other secret data, and without revealing said key to any third party who may have access to all of the transmissions between them. The method has both one-sided and two-sided embodiments. In the one-sided embodiments the two parties agree upon a matrix M, and independently choose matrices S and R from an established commutative family of square matrices. The sender transmits the matrix SM to the receiver and the receiver transmits the matrix RM to the sender. The sender computes the matrix SRM from the received matrix RM, and the receiver computes the matrix RSM from the received matrix SM. Since the matrices S and R commute, SRM=RSM. The value of the matrix SRM is then used to produce the desired cryptographic key. In the two-sided embodiments the two parties agree upon a matrix M, and two commutative families of square matrices F and G.

Abstract: One party sends a securely encrypted message to a second party. Each party chooses a secret message key for the message, which is never shared with or transmitted to any other party. The message is sent by means of three encrypted messages. The first encrypted message is sent from the sender to the receiver, and is encrypted by the sender's key. The second encrypted message is sent from the receiver back to the sender, and is encrypted by both the sender's key and then by the receiver's key. The third encrypted message is sent from the sender back to the receiver, and is encrypted by only the receiver's key following removal of the sender's key. Finally, the receiver decrypts the third message. The messages are sent in blocks. Encryption consists of multiplying each block of the message by square matrices of the same size as the block, and decryption consists of multiplying by the inverse matrices. The key matrices are taken from one or more large commutative families of matrices.

Abstract: One party sends a securely encrypted message to a second party. Each party chooses a secret message key for the message, which is never shared with or transmitted to any other party. The message is sent by means of three encrypted messages. The first encrypted message is sent from the sender to the receiver, and is encrypted by the sender's key. The second encrypted message is sent from the receiver back to the sender, and is encrypted by both the sender's key and then by the receiver's key. The third encrypted message is sent from the sender back to the receiver, and is encrypted by only the receiver's key following removal of the sender's key. Finally, the receiver decrypts the third message. The messages are sent in blocks. Encryption consists of multiplying each block of the message by a square matrix of the same size as the block, and decryption consists of multiplying by the inverse matrix. The key matrices are taken from one or more large commutative families of matrices.

Abstract: A system and method of processing responses to questions presented to an individual. Testing seeks to define what primitive components of the educational program that the individual doesn't understand. Using multiple-choice questions where incorrect answers are derived from failing to process primitives to the problem correctly, the system ensures that every answer to every question defines the problem area for the individual by weighting those primitives against a base threshold when answered incorrectly. Once the threshold has been passed, the system adapts to test the primitive that has failed to be understood. Questions are generated that test to see if the individual understands the theory and concepts associated to the initial primitives' primitive components. The test is complete when there are no further primitives to be examined.

Abstract: A user query is processed to determine a first industry code corresponding to information requested in the query. One or more stored non-keyword-based associations are then used to determine at least one additional industry code which is not a subset or superset of the first industry code. The first and additional industry codes may be in different industry code hierarchies, or in otherwise unrelated portions of the same hierarchy. Information corresponding to the first and additional industry codes is then displayed to the user in response to the query. The display of information for particular industry codes may be based at least in part on a set of weights which indicate relative importance of the corresponding stored associations to users of the system. The weights may be established and maintained by monitoring actual user selections made from previous displays.