CN1192543C - Encryption key exchange method based on public key centificate on elliptic curve - Google Patents
Encryption key exchange method based on public key centificate on elliptic curve Download PDFInfo
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- CN1192543C CN1192543C CNB031166202A CN03116620A CN1192543C CN 1192543 C CN1192543 C CN 1192543C CN B031166202 A CNB031166202 A CN B031166202A CN 03116620 A CN03116620 A CN 03116620A CN 1192543 C CN1192543 C CN 1192543C
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- 238000000034 method Methods 0.000 title claims abstract description 21
- 238000004891 communication Methods 0.000 description 4
- 230000005540 biological transmission Effects 0.000 description 2
- 230000002950 deficient Effects 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000010200 validation analysis Methods 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
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Abstract
The present invention discloses a secret key exchange method based on public key certificates on an elliptic curve. The secret key exchange method is a session secret key exchange method which proceeds from the problem of discrete logarithms on an elliptic curve and a Diffie-Hellman secret key exchange protocol with the assistance of anti-collision hash functions, public key certificates and digital signatures. The secret key exchange method has provable safety and high operation speed.
Description
Technical field
The present invention relates to maintain secrecy or the key exchange method of secure communication, on specifically a kind of elliptic curve based on the key exchange method of public key certificate.
Background technology
Evincible cryptographic algorithm of fail safe and communication protocol are cryptographic important and difficult research topics, and communication security is maintained secrecy and studied around seeking stronger better cryptographic system and launching.Traditional cryptographic system is single key owing to what use when encryption and decryption, in case encryption key is revealed, whole cryptographic system has just lost effect.Therefore exposed increasing defective in actual applications, but since the symmetric key system to have an enciphering rate more faster than public key encryption speed, into have advantage in that mass data is encrypted.Therefore, just produce a kind of mixed encryption method, combined their advantage, promptly used public key encryption system transmission session key, carried out the encryption and decryption of information with session key.Bellovin has designed a kind of method of using symmetry and public key cryptography simultaneously, and this method is encrypted the public-key cryptography that produces at random with cipher key shared.But the EKE agreement has a serious defective, and it needs both sides all to know a shared password P, has limited the scope of communication so greatly.
Summary of the invention
The objective of the invention is to carry on a kind of elliptic curve of arch based on the key exchange method of public key certificate, is discrete logarithm problem from the elliptic curve, is aided with anti-collision hash function, the method for the session key exchange of public key certificate and digital signature.
The concrete steps of the technical solution used in the present invention are as follows:
Because cipher key change is exactly the exchanges of both sides by mutual realization session key, also is related to the identity validation that exchanges both sides.Therefore, it is very natural introducing the user certificate data of representing user identity in cipher key change.Because digital certificate can effectively show subject identity, thereby we obtain a key exchange method based on digital certificate.X.509, the internal form of digital certificate is stipulated that by CCITT it must comprise the information content of the following aspects: the version number of certificate; The sequence number of digital certificate; Certificate owner's name; Signature algorithm; Issue the unit of digital certificate; Issue the signature of the unit of digital certificate; The term of validity of secret key etc. is disclosed. these information are called certificate data (Certificate-data).The concrete steps of key exchange method of the present invention are as follows:
1. system parameters (Fq, E, a P have been defined, n, H), wherein Fq is a finite field, the territory be characterized as big prime number q, E is the elliptic curve on the Fq, P is a rational point on the E, as basic point, the rank of P are prime number n, and H is anti-collision hash function, system parameters (Fq, E, P, n, H) public by one group of user.
2. need the both sides of interchange key to be made as A and B, share the exchange of session key by mutual realization, system parameters be (Fq, E, P, n, H) step of cipher key change is as follows:
(a) A picked at random 1＜r
a＜n calculates u
1=r
aP, and (u
1, sig
A(u
1)) send to B;
(b) the signature u of B checking A
1, Sig
A(u
1), be not inconsistent then termination as signature, otherwise picked at random 1＜r
b＜n calculates u
2=r
bP, and u
2, sig
B(u
1, u
2) send to A, calculating K=H (cert-data, r
bu
1) as session key.
(c) A certifying signature sig
B(u
1, u
2), if sign incorrect then the exchange termination, otherwise calculating K=H (cert-data, r
au
2), as session key;
The present invention compares the beneficial effect that has with background technology: discrete logarithm problem and the Diffie-Hellman IKE of the present invention from the elliptic curve, be aided with anti-collision hash function, the session key exchange method of public key certificate and digital signature.It has evincible fail safe, and has arithmetic speed faster.
Embodiment
When the present invention is used for cipher key change, suppose that user A thinks and communicating by letter that user B maintains secrecy, need on unsafe channel, carry out the transmission of secret meeting words key.In this method, user A and user B use an elliptic curve jointly, and it is as follows to provide an elliptic curve here:
E：y
2＝x
3+ax+b?mod?n
Wherein E is an ellipse garden curve, and a, b are the coefficient of ellipse garden curve, and (x y) is point on the curve of ellipse garden.
Following p is a big prime number, and q is big prime number, and p=2q+1, chooses qualified p and q, can obtain the basic point seedE of ellipse garden curve, and r, a, b are ellipse garden curves of selecting, and n is an ellipse garden order of a curve, selects the ellipse garden curvilinear system of h=1.
p＝6277101735386680763835789423207666416083908700390324961279；
seedE＝0x3045ae6fc8422f64ed579528d38120eae12196d5；
r＝0x3099d2bbbfcb2538542dcd5fb078b6ed5f3d6fe2c745de65；
a＝-3；
b＝0x64210519e59c80e70fa7e9ab72243049feb8deeccl46b9b1；
h＝1
The rank of elliptic curve are:
n＝6277101735386680763835789423176059013767194773182842284081；
It is a prime number.
Rank are that the basic point of n is being chosen for of P:
P=(xG, yG) wherein
xG＝0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012；
yG＝0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811；
User A picked at random 1＜w＜n calculates u=wP, and (u, sig
a(u)) send to B.User B operates according to the step of this method, carries out signature verification, if signature is correct, then picked at random 1＜x＜n calculates y=xP, and (u, y, Sig
b(u, y)) sends to A, and calculating K=(cert-data is xu) as session key.User A certifying signature (u, y, sig
b(u, y)), if sign incorrect promptly stop the exchange, otherwise calculating K=H (cert-data is wy) as session key.
Claims (1)
- On the elliptic curve based on the key exchange method of public key certificate, discrete logarithm difficult problem from elliptic curve is supposed, be aided with the collision hash function, public key certificate (certificate-date) and digital signature method carry out the method for session key exchange, it is characterized in that:1) system parameters (Fq, E, a P have been defined, n, H), wherein Fq is a finite field, the territory be characterized as big prime number q, E is the elliptic curve on the Fq, P is a rational point on the E, as basic point, the rank of P are prime number n, and H is anti-collision hash function, system parameters (Fq, E, P, n, H) open public by one group of user;2) need the both sides of interchange key to be made as A and B, share the exchange of session key by mutual realization, system parameters be (Fq, E, P, n, H), the step of cipher key change is as follows:(a) A picked at random 1＜r a＜n calculates u 1=r aP, and (u 1, sig A(u 1)) send to B;(b) the signature u of B checking A 1, Sig A(u 1), be not inconsistent then termination as signature, otherwise picked at random 1＜r b＜n calculates u 2=r bP, and u 2, sig B(u 1, u 2) send to A, calculating K=H (cert-data, r bu 1) as session key;(c) A certifying signature sig B(u 1, u 2), if sign incorrect then the exchange termination, otherwise calculating K=H (cert-data, r au 2), as session key.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CNB031166202A CN1192543C (en) | 2003-04-23 | 2003-04-23 | Encryption key exchange method based on public key centificate on elliptic curve |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CNB031166202A CN1192543C (en) | 2003-04-23 | 2003-04-23 | Encryption key exchange method based on public key centificate on elliptic curve |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN1455542A CN1455542A (en) | 2003-11-12 |
| CN1192543C true CN1192543C (en) | 2005-03-09 |
Family
ID=29260054
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CNB031166202A Expired - Fee Related CN1192543C (en) | 2003-04-23 | 2003-04-23 | Encryption key exchange method based on public key centificate on elliptic curve |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN1192543C (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101296072B (en) * | 2007-04-29 | 2011-11-09 | 四川虹微技术有限公司 | Sharing cryptographic key generation method of elliptic curve |
| CN101197668B (en) * | 2007-12-06 | 2010-08-18 | 上海交通大学 | Elliptic curve anti-bypass attack method based on randomizing multiplication with symbol scalar |
| CN111106937A (en) * | 2019-12-31 | 2020-05-05 | 深圳职业技术学院 | Secret key exchange method of double-channel exchange super-singular elliptic curve algorithm based on random prime number |
-
2003
- 2003-04-23 CN CNB031166202A patent/CN1192543C/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| CN1455542A (en) | 2003-11-12 |
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