Abstract: Methods and apparatus to limit access to a secure personal network are provided. The method includes receiving an Internet protocol (IP) packet of a device including a confirmation value associated with the SPN. The method compares the confirmation value to a predetermined confirmation value and allows access to the SPN when the confirmation value matches the predetermined confirmation value. The IP packet is dropped otherwise. The confirmation value and the predetermined confirmation value are generated by an algorithm including a pseudorandom number generator, a hash function and a one-time password.

Abstract: A data structure to be used for representing the problem is selected. An instance of the problem is represented with the data structure. The data is encrypted with a sequence which is obtained by solving the problem. Alternatively, in an alternative embodiment of the present invention, a program for heuristically solving an NP-hard problem is received. A data structure that represents an instance of the problem is received. The program is applied to the instance of the problem to obtain a sequence. The data is decrypted with the sequence.

Abstract: A method for calculating greatest common divisors uses an approximate division in its reduction step. The result of this approximate division is then compared to determine if it is valid. If not, then the method applies a correction to the first approximate division to determine corrected values that have a reduced number of bits. If, during this correction step, the result is again not valid, then another method is applied to reduce the number of bits in the values. The approximate division is applied only when the number of significant bits in the two values differ by at least a predetermined number. When the number of bits in the two values differ by less than this number, an alternative GCD algorithm is applied but only to reduce the number of bits in the intermediate values.

Abstract: A method for calculating greatest common divisors and modular inverses using the extended Jebelean GCD algorithm keeps track of the number of times that U3 and V3 have been divided by two in the process of calculating the greatest common divisor and correct the modular inverse for these divisions. The shifting of the binary values representing U3 that occurs during the calculation of the GCD is accomplished by changing the position of respective pointers to bit positions in the binary values rather than implementing a shifting operation.

Abstract: The disclosure is directed to a method of marking for authentication a computer program with a bit-string pattern. The method includes generating a bit-string pattern, each bit in the bit-string pattern having a binary value and at least one bit having a first value. The computer program is searched for at least one polymorphic statement. The one bit having the first value is associated with the polymorphic statement found by the search. The polymorphic statement is then altered, thereby marking the computer program.

Abstract: A method for calculating greatest common divisors and modular inverses using the extended Jebelean GCD algorithm keeps track of the number of times that U3 and V3 have been divided by two in the process of calculating the greatest common divisor and correct the modular inverse for these divisions. The shifting of the binary values representing U3 that occurs during the calculation of the GCD is accomplished by changing the position of respective pointers to bit positions in the binary values rather than implementing a shifting operation.

Abstract: A method for calculating greatest common divisors uses an approximate division in its reduction step. The result of this approximate division is then compared to determine if it is valid. If not, then the method applies a correction to the first approximate division to determine corrected values that have a reduced number of bits. If, during this correction step, the result is again not valid, then another method is applied to reduce the number of bits in the values. The approximate division is applied only when the number of significant bits in the two values differ by at least a predetermined number. When the number of bits in the two values differ by less than this number, an alternative GCD algorithm is applied but only to reduce the number of bits in the intermediate values.

Abstract: A data structure to be used for representing the problem is selected. An instance of the problem is represented with the data structure. The data is encrypted with a sequence which is obtained by solving the problem. Alternatively, in an alternative embodiment of the present invention, a program for heuristically solving an NP-hard problem is received. A data structure that represents an instance of the problem is received. The program is applied to the instance of the problem to obtain a sequence. The data is decrypted with the sequence.