Abstract: A system and method are disclosed for securing binding updates in a wireless telecommunications system. A public key is generating using a home address value of the mobile host. Thereafter, a home agent, such as a router, generates a private key using public cryptographic parameters, that corresponds to the mobile host and the public key. The correspondent node uses the public key to encrypt a shared key and sends the shared key to the mobile host. The mobile host decrypts the shared key using the private key and uses the shared key to sign the binding update. Thereafter, the correspondent node utilizes the shared key to verify the authenticity of the binding update.

Abstract: A plaintext message to be encrypted is segmented into a number of words, e.g., four words stored in registers A, B, C and D, and an integer multiplication function is applied to a subset of the words, e.g., to the two words in registers B and D. The use of such an integer multiplication greatly increases the diffusion achieved per round of encryption, allowing for higher security per round, and increased throughput. The integer multiplication function may be a quadratic function of the form ƒ(x)=x(ax+b), where a is an even integer and b is an odd integer, or other suitable function such as a higher-order polynomial. The results of the integer multiplication function are rotated by 1 g w bits, where 1 g denotes log base 2 and w is the number of bits in a given word, to generate a pair of intermediate results t and u. An exclusive-or of another word, e.g., the word in register A, and one of the intermediate results, e.g., t, is rotated by an amount determined by the other intermediate result u.

Abstract: A plaintext message to be encrypted is segmented into a number of words, e.g., four words stored in registers A, B, C and D, and an integer multiplication function is applied to a subset of the words, e.g., to the two words in registers B and D. The integer multiplication function may be a quadratic function of the form ƒ(x)=x(ax+b) or other suitable function such as a higher-order polynomial. The results of the integer multiplication function are rotated by lg w bits, where lg denotes log base 2 and w is the number of bits in a given word, to generate a pair of intermediate results t and u. An exclusive-or of another word, e.g., the word in register A, and one of the intermediate results, e.g., t, is rotated by an amount determined by the other intermediate result u. Similarly, an exclusive-or of the remaining word in register D and the intermediate result u is rotated by an amount determined by the other intermediate result t.

Abstract: Methods and apparatus for providing secure user identification or digital signatures based on evaluation of constrained polynomials. In an exemplary user identification technique, a prover sends a verifier a commitment signal representative of a first polynomial satisfying a first set of constraints. The verifier sends the prover a challenge signal representative of a second polynomial satisfying a second set of constraints. The prover generates a response signal as a function of (i) information used to generate the commitment signal, (ii) a challenge signal, and (iii) a private key polynomial of the prover, such that the response signal is representative of a third polynomial satisfying a third set of constraints. The verifier receives the response signal from the prover, and authenticates the identity of the prover by evaluating a function of information contained in at least a subset of (i) the commitment signal, (ii) the challenge signal, (iii) the response signal and (iv) a public key of the prover.

Abstract: Methods and apparatus for converting a value A representing in a first basis an element of a finite field GF(q.sup.m) to a value B representing the element in a second basis, where q is a prime number or power of a prime number and m is an integer greater than or equal to 2, and where the value B includes a vector of m coefficients from a finite field GF(q). An exemplary apparatus, particularly well-suited for exporting the value A in an internal basis representation to the value B in an external basis representation, includes an externally shifted sequence generator for generating from the value A a sequence of intermediate values representing in the first basis elements of the finite field GF(q.sup.m) whose representations in the second basis are related to the value B by a predetermined external shift operation. An extractor coupled to the externally shifted sequence generator receives and processes the sequence of intermediate values to generate each coefficient of the value B.