CN1444168A - Probability type asymmetric encipherment method based on public key certificate on ellipse curve - Google Patents

Abstract

The invention discloses a probabilistic asymmetric encryption method based on a public key certificate on an elliptic curve. It starts from the Diffie-Hellman decision problem on the elliptic curve, supplemented by a public-key cryptosystem for encryption and decryption with anti-collision hash functions and public-key certificates. Since the ontology system is constructed on the elliptic curve, its calculation speed is fast and its security is high, and a relatively small key length can guarantee high security. It can be widely used in the technical fields of file encryption and computer network security.

Description

A Probabilistic Asymmetric Encryption Method Based on Public Key Certificate on Elliptic Curve

Technical field

The invention relates to an asymmetric public key encryption method for confidential or safe communication, in particular to a probabilistic asymmetric encryption method based on public key certificates on an elliptic curve.

Background technique

Before the issue of data security and confidentiality was widely recognized, the security and confidentiality of computers referred to the physical security of hardware in the impression of most people. However, today's new technologies such as computer remote terminal access, communication and network have made great progress. In addition to protecting the security of hardware devices, purely physical protection measures have less and less significance for the protection of information and services. Security and confidentiality have become the subject of computer security and confidentiality.

Cryptographic algorithms and communication protocols with provable security are an important and difficult research topic in cryptography. The research on communication security and confidentiality revolves around finding stronger and better cryptosystems. Because the traditional cipher body uses a single key for encryption and decryption, once the encryption key is leaked, the entire cipher system will lose its function. Therefore, more and more defects have been exposed in practical applications, and it is difficult to obtain wider commercial applications. The characteristic of the public key system is that different keys are used for encryption and decryption, one of which is used for encryption and the other is kept secret for decryption. At present, the popular public key encryption system in the world is based on the assumption of large number decomposition and discrete logarithm difficulty. The first practical public key encryption system based on Diffie-Hellman decision problem is proposed by Cramer-Shoup, which has provable security and can resist the attack of adaptively chosen ciphertext.

Contents of Invention

The purpose of the present invention is to provide a probabilistic asymmetric encryption algorithm based on public key certificates on elliptic curves. It starts from the Diffie-Gellman decision problem on the elliptic curve, supplemented by public key certificates and anti-collision hash functions, and performs encryption/decryption public key cryptosystem.

The concrete realization steps of the technical solution adopted in the present invention are as follows:

1. A system parameter (Fq, E, P, n, H) is defined, where Fq is a finite field characterized by a large prime number q, E is an elliptic curve on Fq, and P is a rational point on E, It is called the base point, the order of P is a prime number n, H is an anti-collision hash function, and the system parameter vector (Fq, E, P, n, H) can be shared by a group of users.

2. Randomly select four elements w, x, y, and z smaller than n as the private key vector, and randomly select an element t not greater than n to perform modular multiplication on the elliptic curve E with the base point P. The result g ₁ is used as the public key The first vector of the key, the four components of the private key vector and the first component g ₁ of the public key are respectively subjected to modular multiplication on the elliptic curve E to obtain the other four components of the public key vector, plus the user certificate data Cert-data The six components that constitute the public key vector, the system parameters are (F _q , E, P, n, H), and the steps to generate the private key and public key vector are as follows:

(a) Select t<n, calculate g ₁ =tP as the generating element, as the first component of the public key vector, and randomly select w, x, y, z<n to form the private key vector;

(b) Calculate g ₂ =wg ₁ , c=xg ₁ , d=yg ₁ , h=zg ₁ ;

(c) The private key is (w, x, y, z), and the public key is (g ₁ , g ₂ , c, d, h, Cert-data).

3. Use the recipient’s public key and certificate data to encrypt into a ciphertext vector composed of four components, the system parameters are (Z _p , G, q, H), and the recipient’s public key is (g ₁ , g ₂ , c, d, h, Cert-data), encrypted plaintext m, the encryption steps are:

(a) randomly select r<n;

(b) Calculate u ₁ =rg ₁ , u ₂ =rg ₂ , e=(mrh);

(c) Calculate α=H(Cert-data, u ₁ , u ₂ , e), v=r(c+αd):

(d) The output ciphertext vector is (u ₁ , u ₂ , e, v).

5. After receiving the ciphertext vector, the receiver can check and reject the invalid ciphertext. For valid ciphertext, the receiver’s private key and certificate data can be used to recover the plaintext. The system parameters are (Fq, E, P, n , H), the ciphertext vector is (u ₁ , u ₂ , e, v), the steps of checking and recovering the plaintext are as follows:

(a) Calculate α=H(Cert-data, u ₁ , u ₂ , e);

(b) Check whether u ₂ = wu ₁ is established, if not established, reject the ciphertext, otherwise execute the next step;

(c) Check whether v=(x+yα)u ₁ is established or not, if not established, reject the ciphertext, otherwise execute the next step;

(d) Calculate m=ezu ₁ and recover the plaintext m.

The beneficial effect that the present invention has compared with background technology is:

It starts from the Diffie-Hellman decision problem on the elliptic curve, supplemented by public key certificates and anti-collision hash functions, and performs encryption/decryption public key cryptosystem. Since the ontology system is constructed on the elliptic curve, its calculation speed is fast and its security is high, and a relatively small key length can guarantee high security. It can be widely used in the technical fields of file encryption and computer network security.

Detailed ways

When the present invention is used in network and information confidential communication, it is assumed that sender A wants to send a confidential message to recipient B. The information that this fruit wants to send is exactly the plaintext m, and in the present invention, sender and recipient share an elliptic curve, provide the example that implements on following elliptic curve here:

E: y ² =x ³ +ax+b mod n

in

p=6277101735386680763835789423207666416083908700390324961279;

seedE = 0x3045ae6fc8422f64ed579528d38120eae12196d5;

r = 0x3099d2bbbfcb2538542dcd5fb078b6ed5f3d6fe2c745de65;

a=-3;

b=0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1;

h=1

The order of the elliptic curve is:

n=6277101735386680763835789423176059013767194773182842284081;

It is a prime number.

The selection of the base point P with order n is:

P = (xG, yG) where

xG=0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012;

yG=0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811; User A selects w, x, y, z less than n as his private secret key, and calculates g ₂ =g ₁ ^w , c=g ₁ ^x , d=g ₁ ^y , h=g ₁ ^z respectively. And (g ₁ , g ₂ , c, d, h, Cert-data) is used as a public key and made public, and Cert-data is user certificate data. User B operates according to the steps of this method, and sends the ciphertext. A verifies and decrypts the encrypted information after receiving it.

Claims (5)

1. On the elliptic curve based on the probability type asymmetrical encryption method of public key certificate, it is characterized in that the Diffie-Hellman decision problem from the elliptic curve, be aided with the common key cryptosystem that anti-collision hash function and public key certificate carry out encryption and decryption.
2. 2. based on the probability type asymmetrical encryption method of public key certificate, it is characterized in that having defined a systematic parameter (F on a kind of elliptic curve according to claim 1 _q, E, P, n, H), F wherein _qBe Galois field, the territory be characterized as big prime number q, E is F _qOn elliptic curve, P is a rational point on the E, is called basic point, the rank of P are prime number n, H is anti-collision hash function, systematic parameter vector (F _q, E, P, n H) can be public by one group of user.
3. 3. on a kind of elliptic curve according to claim 2 based on the probability type asymmetrical encryption method of public key certificate, it is characterized in that by four element w less than n, x, y, z selects an element t and a basic point P who is not more than n to carry out the g as a result that the modular multiplication on the elliptic curve E obtains as the private key vector at random ₁As first vector of PKI, four components of private key vector respectively with the first component g of PKI ₁Carry out modular multiplication on the elliptic curve E and obtain other four components of PKI vector, add that user certificate data Cert-data constitutes six components of PKI vector, systematic parameter is (F _q, E, P, n, H), the generation step of its private key and PKI vector is as follows:

   (a) selected t＜n calculates g ₁=tP is a generator, as first component of PKI vector, appoints and gets w, and x, y, z＜n constitutes the private key vector;

   (b) calculate g ₂=wg ₁, c=xg ₁, d=yg ₁, h=zg ₁

   (c) private key be (w, x, y, z), PKI is (g ₁, g ₂, c, d, h, Cert-data).
4. 4. based on the probability type asymmetrical encryption method of public key certificate, it is characterized in that utilizing recipient's PKI and certificate data to be encrypted to the ciphertext vector of being made up of four components on a kind of elliptic curve according to claim 2, systematic parameter is (Z _p, G, q, H), PKI is (g ₁, g ₂, c, d, h, Cert-data), and encrypting plaintext m, encrypting step is:

   (a) picked at random r＜n;

   (b) calculate u ₁=rg ₁, u ₂=rg ₂, e=(m rh);

   (c) calculate α=H (Cert-data, u ₁, u ₂, e), v=r (c+ α d);

   (d) output ciphertext vector is (u ₁, u ₂, e, v).
5. 5. on a kind of elliptic curve according to claim 2 based on the probability type asymmetrical encryption method of public key certificate, after it is characterized in that the recipient arrives the ciphertext vector, can check and refuse invalid ciphertext, then can utilize recipient's private key and certificate data to recover expressly for effective ciphertext, systematic parameter is (Fq, E, P, n, H), the ciphertext vector is (u ₁, u ₂, e, v), expressly step is as follows for its check and recovery:

   (a) calculate α=H (Cert-data, u ₁, u ₂, e);

   (b) check u ₂=wu ₁Whether set up, as the refusal ciphertext that is false, otherwise carry out next step;

   (c) check v=(x+y α) u ₁Whether set up, as be false and then refuse ciphertext, otherwise carry out next step;

   (d) calculate m=e zu ₁, recover expressly m.