Information authentication method and information authentication system

An information authentication method in an authentication of information performed by a client terminal and an authentication server, comprising:

• at a time of enrollment,
• the steps, performed by the client terminal, of
• acquiring information for enrollment via an input unit;
• generating, based on the information for enrollment, a first feature polynomial a which features the information for enrollment;
• generating a mask polynomial s randomly;
• generating a template polynomial φ that has an inverse polynomial which is modulo a prescribed integer and a prescribed polynomial and which is an inverse with respect to a modular multiplication of a polynomial, and that has a norm equal to or smaller than a preset value;
• calculating a helper polynomial h=(s+pa)*φ−1 by adding a product of a prescribed integer p and the first feature polynomial a to the mask polynomial s, and, further multiplying the addition result by the inverse polynomial φ−1 of the template polynomial φ;
• storing the calculated helper polynomial h and the mask polynomial s in a storage part of the client terminal itself;
• transmitting the template polynomial φ to the authentication server;
• and
• the step, performed by the authentication server upon receipt of the template polynomial φ, of,
• storing the received template polynomial φ in a storage medium;
• and,
• at a time of authentication,
• the steps, performed by the client terminal, of,
• acquiring information for authentication via the input part;
• generating, based on the information for authentication, a second feature polynomial b which features the information for authentication;
• generating a first random polynomial which has a norm equal to or smaller than a preset value;
• calculating an authentication polynomial v=hb+ψ and w=sb;
• transmitting the calculated authentication polynomials v, w to the authentication server;
• and
• the steps, performed by the authentication server upon receipt of the authentication polynomials v, w, of,
• acquiring the template polynomial φ from the storage medium;
• calculating a polynomial of c″=vφ−w, dividing the polynomial c″ by the prescribed integer p, and calculating a polynomial c′ by extracting an integer portion of each coefficient of a set term;
• and
• taking each coefficient of the set term from among c′ as a degree of similarity, comparing the degree of similarity with a preset threshold, and thereby determining a match or a nonmatch between the information for enrollment and the information for authentication.

An information authentication method in an authentication of information performed by a client terminal and an authentication server, comprising:

• at a time of enrollment,
• the steps, performed by the client terminal, of
• acquiring information for enrollment via an input unit;
• generating, based on the information for enrollment, a first feature data which is an array featuring the information for enrollment;
• generating a first feature polynomial a which is a polynomial having each array of the feature data as a coefficient;
• generating a mask polynomial s randomly;
• generating a template polynomial φ that has a norm which is a maximum value of an absolute value of a coefficient is equal to or smaller than a prescribed value, has the number of non-zero coefficients equal to or smaller than a prescribed number, and has a polynomial as an inverse;
• calculating a helper polynomial h=(s+pa)φ−1 using a prescribed integer p;
• storing the helper polynomial h and the mask polynomial s in a storage unit and transmitting the template polynomial φ to the authentication server;
• the step, performed by the authentication server upon receipt of the template polynomial φ, of
• storing the received template polynomial φ in a storage medium;
• and,
• at a time of authentication,
• the steps, performed by the client terminal, of
• acquiring information for authentication via the input part;
• generating, based on the information for authentication, a second feature data which is an array featuring the information for authentication;
• generating a second feature polynomial b which is a polynomial having each array of the feature data as a coefficient;
• generating a random polynomial ψ that has a norm which is a maximum value of an absolute value of a coefficient equal to or smaller than a prescribed value, and has the number of non-zero coefficients equal to or smaller than a prescribed number;
• generating a random polynomial r that has a random finite value as a coefficient, although a value of a coefficient of a set term which is a term previously set takes a random finite value equal to or smaller than a prescribed value, and that is different from the random polynomial ψ;
• calculating authentication polynomials v=hb+ψ and w=sb−r;
• transmitting the calculated authentication polynomials v, w to the authentication server;
• and
• the steps, performed by the authentication server upon receipt of the authentication polynomials v, w, of
• acquiring the template polynomial φ from the storage medium;
• calculating a polynomial of c″=vφ−w, dividing the polynomial c″ by the prescribed integer p, and calculating a polynomial c′ by extracting an integer portion of each coefficient of a set term;
• and
• taking the each coefficient of the set term from among c′ as a degree of similarity, comparing the degree of similarity with a preset threshold, and thereby determining a match or a nonmatch between the information for enrollment and the information for authentication.

An information authentication system in an authentication of information performed by a client terminal and an authentication server, comprising:

• the steps, performed by the client terminal, of,
• at a time of enrollment,
• acquiring information for enrollment via an input unit;
• generating a first feature polynomial based on the information for enrollment;
• calculating a helper polynomial by:
• multiplying the first feature polynomial by a prescribed integer;
• generating a template polynomial, the template polynomial being a polynomial that has an inverse polynomial which is modulo a prescribed integer and a prescribed polynomial and which is an inverse with respect to a modular multiplication of a polynomial, and that has a norm equal to or smaller than a preset value;
• and further multiplying the multiplied first feature polynomial by the inverse polynomial of the template polynomial;
• storing the helper polynomial in a storage part of the client terminal itself and transmitting the template polynomial to the authentication server;
• and
• at a time of authentication,
• acquiring information for authentication via the input unit;
• generating a second feature polynomial based on the information for authentication;
• generating a first random polynomial which has a norm equal to or smaller than a preset value;
• calculating a first authentication polynomial by multiplying the helper polynomial by the second feature polynomial and adding the first random polynomial to the multiplication result;
• transmitting the first authentication polynomial to the authentication server;
• and
• the steps, performed by the authentication server, of,
• at the time of enrollment,
• upon receipt of the template polynomial from the client terminal, storing the received template polynomial in a storage medium;
• and,
• at the time of authentication,
• upon receipt of the first authentication polynomial from the client terminal, multiplying the first authentication polynomial by the inverse polynomial of the template polynomial and dividing the multiplication result by the prescribed integer;
• and
• determining a match or a nonmatch between the information for enrollment and the information for authentication, based on the division result.