CN1455542A - 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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- CN1455542A CN1455542A CN 03116620 CN03116620A CN1455542A CN 1455542 A CN1455542 A CN 1455542A CN 03116620 CN03116620 CN 03116620 CN 03116620 A CN03116620 A CN 03116620A CN 1455542 A CN1455542 A CN 1455542A
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- key
- elliptic curve
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- public key
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Abstract
The exchange method is based on discrete-logarithm issue and Diffie-Hellman cipher key exchange protocol on the elliptical curve and assisted with anti-impact odds and ends function, session key exchange method of public key certificate and digital signature. The method is good at security which can be certified and it has quick 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, be called 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
p＝6277101735386680763835789423207666416083908700390324961279；
seedE＝0x3045ae6fc8422f64ed579528d38120eae12196d5；
r＝0x3099d2bbbfcb2538542dcd5fb078b6ed5f3d6fe2c745de65；
a＝-3；
b＝0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1；
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 the session decryption key.
Claims (3)
- On the elliptic curve based on the key exchange method of public key certificate, it is characterized in that the discrete logarithm difficult problem hypothesis from the elliptic curve, be aided with the collision hash function, public key certificate (certificate-date) and digital signature method carry out the method for session key exchange.
- 2. based on the key exchange method of public key certificate, it is characterized in that having defined system parameters (Fq, an E on a kind of elliptic curve according to claim 1, P, 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, is called basic point, and the rank of P are prime number n, H is anti-collision hash function, system parameters (Fq, E, P, n, H) public by one group of user.
- 3. based on the key exchange method of public key certificate, needing it is characterized in that the both sides of interchange key to be made as A and B on a kind of elliptic curve according to claim 2, share the exchange of session key by mutual realization, system parameters is (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 true CN1455542A (en) | 2003-11-12 |
| CN1192543C 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 |
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|---|---|
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| 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 |
| 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
Cited By (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 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN1192543C (en) | 2005-03-09 |
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