KR0137536B1 - Electronic signature method with a sell-inspection characteristic - Google Patents

Abstract

The present invention relates to a digital electronic signature method based on personal identification information having self-certification characteristics. The present invention solves a stability problem based on a high residual filter problem and a discrete algebra problem, and the center knows each user's secret key. A first step (21) of initializing a coefficient to provide a new digital signature method based on self-identifying personal identification information which cannot be verified and which is not required by the authenticator; A second step 22 of selecting the personal identification information I as a public key; A third step (23) of calculating verification information (i, x); A fourth step (24 to 27) for selecting a random number r and calculating a signature intermediate value v, a hash function result e and signature information z for plain text; And a fifth step (28, 29) in which the verifier calculates the hash function and then verifies the verification function after calculating the verification median value (v). There is an effect that can not meet the minimum recognition conditions.

Description

Non-interactive digital signature method based on personally identifiable information with self-authentication characteristics.

1 is a block diagram of a system to which the present invention is applied,

2 is a flow chart in accordance with the present invention.

* Explanation of symbols for the main parts of the drawings

11: Computer network 12: Computer

13: personal computer

The present invention relates to a digital electronic signature method based on personally identifiable information with self-certifying characteristics, and in particular, an identity-based method based on the concept of a self-certified public key. This is applied to the personal identification information itself is a public key.

Innovative developments in software technology and semiconductor technology have made computer processing more common. Accordingly, with the development of advanced information processing technology and information and communication technology, the information society has come. To do this, all current business needs to be transformed to fit the society, and digital signature is one of them. Digital signatures are electronic representations of the seals and signatures currently in use.

The conventional digital signature method is mainly implemented using a public key cryptographic algorithm. At this time, the public key of each user is divided into a method based on an authenticator and a method based on personal identification information.

The method of using personal identification information is called an identity-based method, and the method using an authenticator is called a certification-based method.

In a certificate-based approach, the center uses the certifier CA, which encrypts user A's public key P _A and the pair of personally identifying information Id _A (P _A , I _A ) with the center's private key. Distribute to User A uses a CA to authenticate his public key to other users.

However, in the identity-based scheme, since user A's personal identification information Id _A becomes a public key, no special authentication procedure is required.

The important differences between the certification-based approach and the identity-based approach are as follows.

In a certificate-based scheme, even the center cannot know each user's private key, but in an identity-based scheme, the center can know every user's private key. .

M. Girault proposed an identity-based approach that is not only an identity-based approach but also a paradoxical personal identification that the center does not know each user's secret key. However, the proposed method is not strictly an identity-based method by using an authenticator in a strict sense.

Furthermore, M. Girault introduces the concept of a self-certified public key, an intermediate between identity-based and certificate-based methods. It was. In the self-certified public key method, a certifier exists but the public key itself acts as a certifier.

Gurault also defined the type of trust.

Type 1

If the center knows all users' private keys

Type 2

The center cannot know each user's private key, but can mimic any user.

Type 3

The center cannot know each user's private key and cannot imitate any user. Not being able to imitate here means that you can imitate, but you can later discover the center's misconduct.

As described above, the conventional digital signature method is implemented by a signature method based on an authenticator and a signature method based on personal identification information.

Thus, there is a need for a new digital signature method that does not allow the center to know each user's secret and requires no authenticator.

The present invention devised to meet the above needs solves the stability problem based on the high surplus problem and the discrete algebra problem, and the advantages of the certificate-based signature method Based on a new concept of self-certified identity that takes full advantage of identity-based signature schemes (no authenticator required) and private-identity signatures. The purpose is to provide a new digital signature method.

In order to achieve the above object, the present invention provides a plurality of personal computers connected to each user; A computer acting as a center; And a method applied to a device having a computer network connecting the computers to each other, the method comprising: a first step of initializing coefficients of a system; After performing the first step, the user selects an arbitrary number (s) as the secret key, selects the personal identification information (I) as the public key, and modulo n (n is any two prime numbers p, calculating a value (b ^s ) of a product of q) and transmitting a modular n value for the public and private keys to a center; After performing the second step, the center calculates and transmits verification information (i, x) to the user; After performing the third step, the user selects a random number r, calculates a signature intermediate value v and a hash function result e, calculates signature information z for plain text, and then verifies the verifier. Transmitting a verification information (i, x), a hash function result (e), and signature information (z) for the plain text to the user; And after performing the fourth step, the verifier includes a fifth step of calculating and verifying a hash function after calculating the verification intermediate value v.

Hereinafter, with reference to the accompanying drawings will be described an embodiment according to the present invention;

1 is a configuration diagram of a system to which the present invention is applied and includes a plurality of personal computers 13 to which each user connects, a computer 12 for center dynamics, and a computer network 11 connecting the computers. It is provided.

The present invention is applicable to all general computer network environments, and is particularly non-interactive, so that the present invention can be applied to a network consisting of one-way communication.

2 is a flow chart according to the present invention.

In order to explain a digital signature method based on personal identification information having a self-certifying characteristic of the present invention, a basic arrangement will first be described.

Referred residues (γ ^th -residue) - amount of the constant γ, z n integer time is given if any of the following conditions: γ ^th.

[Condition] There exists x that gcd (z, n) = 1 and satisfies z ≡ x ^γ mod n.

Z do not satisfy the above conditions is γ ^th - referred to as non-residues (γ ^th -nonresidue).

γ ^th - to determine the residues (γ ^th -Residuosity) - residues (γ ^th -Residuosity) problem (γ ^th -RP) it is γ ^th given a positive integer _n z∈Z ^2.

When n is a prime number, the above problem is easily solved. However, the above problem is known to be very difficult when the prime factor of n is unknown.

When (n, γ, y) satisfies the following three conditions, it is called acceptable.

(Condition 1) n = n ₁ n ₂ .... n _t , where each n ₁ is an odd fractional number.

(Condition 2) γ is equal to gcd (γ, , (n ₁ )) = γ and gcd (γ, is an odd number greater than 2, where (n _i )) = 1.

(Condition 3) , Where all i 0eγ, gcd (e, γ) = 1, 1≤b _j ≤ 1, 1≤j≤t (n _j ) and h ₁ , h ₂ , ..... ht is the generator-vector of Z _n ² .

Given an acceptable triple (n, γ, y) and z ∈ Zn ² , i satisfying z = y ¹ u ^γ mod n is the class-index of z. It is called.

There are two different problems associated with γ ^th -RP.

(1) γ ^th -RP

(2) Class-index-comparing problem: a class of z when one acceptable (n, γ, y) and z ₁ , z ₂ ∈Z _n ² are given -Problems comparing class-index

(3) Class-index-finding problem: a class of z given an acceptable triple (n, γ, y) and z∈Z _n ^2- Problems comparing class-index

Zheng proved the following relationship:

(a) The problem of γ ^th -RP and Class-index-comparing is equivalent.

(b) The γ ^th -RP and Class-index-comparing problems result in a Class-index-finding problem.

(c) For γ = 0 (poly (k)), the γ ^th -RP and Class-index-finding problem are equivalent to the Class-index-finding problem.

Park Seong-jun and two others extended the relationship (c) above and demonstrated the following relationship (c ').

(c ') In this case, the problem of γ ^th -RP and class-index-comparing is equivalent to the class-index-finding problem.

Hereinafter, a digital electronic signature method based on personal identification information having a self-authentication characteristic will be described.

о system initialization

Let n be the product of two prime numbers p, q. p, q satisfies the following form.

p = 2γ ^s p '+ 1 and q = 2fq' + 1

Where f, p ', q' are different prime numbers, gcd (γ, q ') = 1, gcd (γ, f) = 1.

the y (γ ^{s) th} - non residues ((γ ^{s) th} -nonresidue) laying a mod n, (n, γs, y) is a block acceptor triple (acceptable triple), modular (modulo) n on the b The order of is f.

The public key of the center is (n, γ ^s , y, b, f) and the secret key of the center is (p ', q') (21).

User A chooses a random number s less than f as his private key, calculates b ^s mod n with his identity I as its public key, and sends I and b ^s from the center (22). .

The center

Calculate i and x that satisfy I is the class-index of (Ib ^s ) ^-1 (mod n). Then, the obtained i and x are distributed to the user. Where i and x need not be secret (23).

Digital digital signature scheme based on personally identifiable information with self-certifying characteristics: The process by which user A signs plaintext m and verifies by user B.

User A signs plaintext m in the following protocol:

1) User A selects a random number r on [0, f-1] (24).

2) Calculate v = b ^r (mod n) and e = h (v, m). Where h is the hash function (25).

3) User A computes z = r + se (mod f) (26) and sends z, i, x, e to User B (27).

4) User B Calculate (28).

5) User B verifies e = h (v, m) (29).

The operation in the center during the initialization process of the system of the present invention may be as follows.

The center

I = f (b, s, y, x) (mod n)

Calculate i and x that satisfy I is the class-index of (Ib ^s ) ^-1 (mod n). Then, the obtained i and x are distributed to the user. Where i and x need not be secret.

An example of a formula satisfying i is as follows.

Yes)

The present invention as described above has the following effects.

First, user B verifies the signature with probability 1. (Completeness)

Second, any user C who does not know the secret key s cannot generate a signature. (Soundness: soundness)

Third, it satisfies the minimum knowledge requirement.

Claims (9)

A plurality of personal computers 13 to which each user connects; A computer 12 serving as a center; And a method applied to a device having a computer network (11) for interconnecting the computers, comprising: a first step (21) of initializing coefficients of a system; After performing the first step 21, the user selects a random number s as the private key, selects the personal identification information I as the public key, and modulo n (n for the secret key) A second step (22) of calculating a value (b ^s ) of a product of a prime number p, q) and transmitting a modular n value for the public and private keys to a center; After performing the second step 22, the center calculates and transmits verification information (i, x) to the user (23); After performing the third step (23), the user selects a random number (r), calculates the signature intermediate value (v) and the hash function result value (e), and then calculates the signature information (z) for the plain text. A fourth step (24 to 27) for transmitting the verification information (i, x), the hash function result (e) and the signature information (z) for the plain text to the verifier at; And after performing the fourth steps 24 to 27, the verifier includes fifth steps 28 and 29 for calculating and verifying a hash function after calculating the verification intermediate value v. Non-interactive digital signature method based on personally identifiable information. The method of claim 1, wherein the first step 21 is n = pq, p = 2γ ^s p '+ 1, q = 2fq' + 1, gcd (γ, q ') = 1, gcd (γ, f) = 1, y is (γ ^s ) ^th -non-surplus ((γ ^s ) ^th -nonresidue) mod n, and (n, γ ^s , y) is an acceptable triple F is the order of b on modulo n, and f, p ', q' are (n, γ ^s , y, b, f) satisfying different prime numbers as the public key of the center. And (p ', q') as the private key of the center. Non-interactive digital signature method based on personal identification information having a self-authentication characteristic. The verification information of the third step 23 ^satisfies I = b ^-s y ^-i x ^-γs (mod n) (b: primitive element for the module f, γ: odd constant). Non-interactive electronic signature method based on personally identifiable information having a self-authentication characteristic. The personal identification information having the self-identification property of claim 1, wherein the random number r of the fourth steps 24 to 27 is selected between 0 and a number less than 1 to a random number f. Non-interactive electronic signature method based on. The method of claim 1, wherein the signature intermediate value v of the fourth steps 24 to 27 is such that v = b ^r (mod n) (r: random number, b: odd constant) is satisfied. Non-interactive digital signature method based on personally identifiable information with a self-authentication characteristic. The signature information (z) for the plain text of the fourth step (24 to 27) is: z = r + se (mod f) (r: random number, e: result of the hash function, f: Non-interactive digital signature method based on personally identifiable information having a self-authentication characteristic. The method of claim 1, wherein the verification intermediate value (v) of the fifth step (28, 29), (y: (γ ^s ) ^th -non-excess mod n, γ: odd constant) is a non-interactive electronic signature method based on personally identifiable information characterized in that it satisfies. According to claim 1, wherein the verification information of the third step (23), (b: primitive element for module f, γ: odd constant) A non-interactive digital signature method based on personally identifiable information with self-identification characteristics. According to claim 1, wherein the verification information of the third step (23), (b: primitive element for module f, γ: odd constant) A non-interactive digital signature method based on personally identifiable information with self-identification characteristics.