Patents by Inventor Kazmaro Aoki

Kazmaro Aoki has filed for patents to protect the following inventions. This listing includes patent applications that are pending as well as patents that have already been granted by the United States Patent and Trademark Office (USPTO).

  • Scheme for arithmetic operations in finite field and group operations over elliptic curves realizing improved computational speed
    Patent number: 6266688
    Abstract: A scheme for arithmetic operations in finite field and group operations over elliptic curves capable of realizing a very fast implementation. According to this scheme, by using a normal basis [&agr; &agr;+1], the multiplicative inverse calculation and the multiplication in the finite field GF(22n) can be realized as combinations of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2n). Also, by using a standard basis [1 &agr;], the multiplication, the square calculation, and the multiplicative inverse calculation in the finite field GF(22n) can be realized as combinations of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2n). These arithmetic operations can be utilized for calculating rational expressions expressing group operations over elliptic curves that are used in information security techniques such as elliptic curve cryptosystems.
    Type: Grant
    Filed: August 14, 2000
    Date of Patent: July 24, 2001
    Assignee: Nippon Telegraph and Telephone Corporation
    Inventors: Kazmaro Aoki, Kazuo Ohta
  • Scheme for arithmetic operations in finite field and group operations over elliptic curves realizing improved computational speed
    Patent number: 6202076
    Abstract: A scheme for arithmetic operations in finite field and group operations over elliptic curves capable of realizing a very fast implementation. According to this scheme, by using a normal basis [&agr; &agr;+1], the multiplicative inverse calculation and the multiplication in the finite field GF(22n) can be realized as combinations of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2n). Also, by using a standard basis [1 &agr;], the multiplication, the square calculation, and the multiplicative inverse calculation in the finite field GF(22n) can be realized as combinations of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2n). These arithmetic operations can be utilized for calculating rational expressions expressing group operations over elliptic curves that are used in information security techniques such as elliptic curve cryptosystems.
    Type: Grant
    Filed: January 18, 2000
    Date of Patent: March 13, 2001
    Assignee: Nippon Telegraph and Telephone Corporation
    Inventors: Kazmaro Aoki, Kazuo Ohta