Conference session key distribution method in an ID-based cryptographic system

1. A method of operating an ID-based cryptographic system via a computer, the ID-based cryptographic system including a session initiating party and a plurality of session participating parties, by distributing a session shared key for encryption from the session initiating party to the plurality of session participating parties in a single conference session via the computer, the method comprising:

(a) generating two temporary secret keys for the session initiating party, two temporary public keys for the session initiating party, and a signature value obtained by applying a predetermined signature function to the two temporary public keys for the session initiating party;

(b) sending a message, including ID information of the session initiating party, the two temporary public keys for the session initiating party, and the signature value, to each session participating party;

(c) receiving messages, including two temporary public keys for each session participating party, from each session participating party, and determining validity of the messages;

(d) generating shared key generation variables for each session participating party that has sent a valid message;

(e) generating the session shared key and encrypting the ID information of the session initiating party using the session shared key; and

(f) sending a message including the shared key generation variables and the encrypted ID information to each session participating party that has sent a valid message.

2. The method of operating the ID-based cryptographic system as claimed in claim 1 ,

wherein the ID-based cryptographic system is a system satisfying an equation y s i =α ƒ(ID i ) (r i r i ) −1 mod q on a finite group G having an order p, that is, a partial group of GF(q)*, wherein q is a sufficiently large prime number and the associated integer q−1 has p as its factor, and wherein parameters y, α, f, r i , s i , and ID i are a public key of a key authentication center, a generation source of the finite group G, a hash function, a public key for a party i, a secret key for the party i, and ID information, respectively, and

wherein step (a) comprises:

(a1) randomly selecting temporary secret keys u 1 and v 1 between 1 and p−1;

(a2) generating temporary public keys w 1 =y v 1 (mod q) and n 1 =w 1 u 1 (mod q); and

(a3) generating the signature value η 1 =(ƒ(n 1 , ID 1 , time)−v 1 w 1 )s 1 −1 (mod p), wherein parameters ID 1 and time are ID information of the session initiating party and time information.

3. The method of operating a then ID-based cryptographic system as claimed in claim 2 , wherein step (a1) comprises:

(a11) randomly selecting the first temporary secret key u 1 between 1 and p−1; and

(a12) generating the second temporary secret key v 1 by applying the hash function to the first temporary secret key u 1 .

4. The method of operating the ID-based cryptographic system as claimed in claim 2 , wherein step (c) comprises:

(c1) receiving messages (ID j , r j , w j , n j , η j ) from each session participating party, wherein parameters ID j , r j , w j , n j , and η j are ID information of each party j, a permanent public key of each party j, temporary public keys generated by each party j, and a signature value generated by each party j; and

(c2) determining whether a message received from each party j satisfy an equation y ƒ(n j ) =w j w j (α EID j r j −r j ) η j (mod q), wherein EID j =f(ID j ).

5. The method of operating the ID-based cryptographic system as claimed in claim 4 , wherein step (d) includes generating the public key generation variable z j =(n 1 ·n j ) u 1 (mod q) for each session participating party having sent a message which satisfies the equation in step (c2).

6. The method of operating the ID-based cryptographic system as claimed in claim 4 , wherein step (e) comprises:

(e1) generating the session shared key K C =n 1 u 1 (mod q); and

(e2) encrypting the ID information of the session initiating party using the session shared key to generate E Kc (ID 1 ), where E is an encryption algorithm.

7. The method of operating the ID-based cryptographic system as claimed in claim 1 ,

wherein the ID-based cryptographic system is a system using a Weil Pairing operation in a finite elliptic curve encryption group G having a sufficiently large prime number p as an order,

wherein step (a) comprises:

(a1) randomly selecting temporary secret keys u 1 and v 1 between 1 and p−1;

(a2) generating temporary public keys w 1 =[v 1 ]α and n 1 =[u 1 ]w 1 , wherein the parameter α is a generation source of the finite elliptic curve encryption group G; and

(a3) generating the signature value η 1 =[v 1 −1 ]([ƒ 2 (ƒ 3 (n 1 ), ID 1 , time)]α[ƒ 3 (w 1 )]s 1 ), where f 2 , f 3 , ID 1 , time, and s 1 are a hash function defined in an integer domain, a hash function defined in the finite elliptic curve encryption group G, ID information of the session initiating party, time information, and a permanent secret key of the session initiating party, respectively.

8. The method of operating the ID-based cryptographic system as claimed in claim 7 , wherein step (a1) comprises:

(a11) randomly selecting the first temporary secret key u 1 between 1 and p−1; and

(a12) generating the second temporary secret key v 1 by applying the hash function to the first temporary secret key u 1 .

9. The method of operating the ID-based cryptographic system as claimed in claim 7 , wherein step (c) comprises:

(c1) receiving messages (ID j , w j , n j , η j ) from each session participating party, wherein parameters ID j , w j , n j , and η j are ID information of each party j, temporary public keys generated by each party j, and a signature value generated by each party j, respectively; and

(c2) determining whether a message received from each party j satisfies an equation, e(w j , η j )=e(α,[ƒ 3 (n j )]α)·e(y,[ƒ 3 (w j )]r j ) where e, y, and r j are a Weil Pairing function defined on an elliptic curve, a public key of a key authentication center, and a permanent public key of each session participating party j, respectively.

10. The method of operating the ID-based cryptographic system as claimed in claim 9 , wherein step (d) includes generating the public key generation variable z j =[u 1 ](n 1 +n j ) for the session participating parties having sent a message that satisfies the equation in step (c2).

11. The method of operating the ID-based cryptographic system as claimed in claim 9 , wherein step (e) comprises:

(e1) generating the session shared key K C =[u 1 ]n 1 ; and

(e2) encrypting the ID information of the session initiating party using the session shared key to generate E Kc (ID 1 ), wherein E is an encryption algorithm.

12. A method of operating an ID-based cryptographic system via a computer, the ID-based cryptographic system including a session initiating party and a plurality of session participating parties, by distributing a session shared key for encryption from the session initiating party to the plurality of session participating parties in a single conference session via the computer, the method comprising:

(a) receiving a message, including ID information, a temporary public key, and a predetermined signature value of the session initiating party, from each session participating party, and determining validity of the message;

(b) generating two temporary secret keys for each session participating party, two temporary public keys for each session participating party, and a signature value obtained by applying a predetermined signature function to the two temporary public keys for each session participating party;

(c) sending a message, including the temporary public keys for each session participating party and the signature value, to the session initiating party;

(d) receiving a message, including a shared key generation variable and encrypted ID information of the session initiating party, from the session initiating party;

(e) generating the session shared key using the shared key generation variable and the temporary secret keys for each session participating party; and

(f) decrypting the encrypted ID information of the session initiating party using the session shared key, and determining whether the session shared key is valid.

13. The method of operating the ID-based cryptographic system as claimed in claim 12 ,

wherein the ID-based cryptographic system is a system satisfying an equation y s i =α ƒ(IDi) (r i r i ) −1 mod q on a finite group G having an order p, that is, a partial group of GF(q)*, wherein q is a sufficiently large prime number and the associated integer q−1 has p as its factor, and wherein parameters y, α, f, r i , s i , and ID i are a public key of a key authentication center, a generation source of the finite group G, a hash function, a public key for a party i, a secret key for the party i, and ID for the party i, respectively,

wherein step (b) comprises:

(b1) randomly selecting temporary secret keys u j and v j between 1 and p−1;

(b2) generating temporary public keys w 1 =y v 1 (mod q) and n 1 =w 1 u 1 (mod q); and

(b3) generating the signature value η 1 =(ƒ(n 1 , ID 1 , time)−v 1 w 1 )s 1 −1 (mod p).

14. The method of operating the ID-based cryptographic system as claimed in 13 , wherein step (b1) comprises:

(b11) randomly selecting the first temporary secret key u j between 1 and p−1; and

(b12) generating the second temporary secret key v j by applying the hash function to the first temporary secret key u j .

15. The method of operating the ID-based cryptographic system as claimed in 13 , wherein step (a) comprises:

(a1) receiving a message (ID 1 , r 1 , w 1 , n 1 , η 1 , time) from the session initiating party, wherein parameters ID 1 , r 1 , w 1 , n 1 , η 1 , and time are ID information of the session initiating party, a permanent public key of the session initiating party, temporary public keys generated by the session initiating party, a signature value generated by the session initiating party, and time information; and

(a2) determining whether the message satisfies an equation y ƒ(n 1 , ID 1 , time) =w 1 w 1 (α EID 1 r 1 −r 1 ) η 1 (mod q), where EID 1 =ƒ(ID 1 ).

16. The method of operating the ID-based cryptographic system as claimed in claim 15 , wherein step (e) includes generating the session shared key K C =z j ·(n 1 u j ) −1 (mod q), where z j is the shared key generation variable received from the session initiating party.

17. The method of operating the ID-based cryptographic system as claimed in claim 12 ,

wherein the ID-based cryptographic system is a system using a Weil Pairing operation in a finite elliptic curve encryption group G having a sufficiently large prime number p as an order, and

wherein step (b) comprises:

(b1) randomly selecting temporary secret keys u j and v j between 1 and p−1;

(b2) generating temporary public keys w j =[v j ]α and n j =[u j ]w 1 , wherein the parameters α is a generation source of the finite elliptic curve encryption group G; and

(b3) generating the signature value η j =[v j −1 ]([ƒ 3 (n j )]α+[ƒ 3 (w j )]s j ), wherein f 3 and s j are a hash function defined in the finite elliptic curve encryption group G and a permanent secret key of the party j, respectively.

18. The method of operating the ID-based cryptographic system as claimed in claim 17 , wherein step (b1) comprises:

(b11) randomly selecting the first temporary secret key u j between 1 and p−1; and

(b12) generating the second temporary secret key v j by applying the hash function to the first temporary secret key u j .

19. The method of operating the ID-based cryptographic system as claimed in claim 17 , wherein step (a) comprises:

(a1) receiving a message (ID 1 , w 1 , n 1 , η 1 , time) from the session initiating party, wherein parameters ID 1 , w 1 , n 1 , η 1 and time are ID information of the session initiating party, temporary public keys generated by the session initiating party, a signature value generated by the session initiating party, and time information; and

(a2) determining whether the message satisfies an equation e(w 1 , η 1 )=e(α,[ƒ 2 (ƒ 3 (n 1 ), ID 1 , time)]α·e(y,[ƒ 3 (w 1 )]r 1 ), wherein e, f 2 , f 3 , y, and r 1 are a Weil Pairing function defined on an elliptic curve, a hash function defined in an integer domain, a hash function defined in the finite elliptic curve encryption group G, a public key of a key authentication center, and a permanent public key of the session initiating party, respectively.

20. The method of operating the ID-based cryptographic system as claimed in claim 19 , wherein step (e) includes generating the session shared key K C =z j −[u j ]n 1 , where z j is the shared key generation variable received from the session initiating party.

21. The method of operating the ID-based cryptographic system as claimed in claim 12 , wherein step (f) comprises:

(f1) decrypting the encrypted ID information of the session initiating party received from the session participating party using the session shared key; and

(f2) determining whether the decrypted ID information of the session initiating party is identical to the ID information of the session initiating party received in step (a).

22. A computer-readable storage medium on which a program is recorded, wherein the program is executed in a computer, the program comprising:

(a) generating two temporary secret keys for the session initiating party, two temporary public keys for the session initiating party, and a signature value obtained by applying a predetermined signature function to the two temporary public keys for the session initiating party;

(b) sending a message, including ID information of the session initiating party, the temporary public keys for the session initiating party, and the signature value, to each session participating party;

(c) receiving a message, including the temporary public keys for each session participating party, from each session participating party, and determining validity of the messages;

(d) generating shared key generation variables for each session participating party that has sent a valid message;

(e) generating a session shared key and encrypting the ID information of the session initiating party using the session shared key; and

(f) sending a message, including the shared key generation variables and the encrypted ID information, to each session participating party that has have sent a valid message.

23. A computer-readable storage medium on which a program is recorded, wherein the program is executed in a computer, the program comprising:

(a) receiving a message, including ID information, a temporary public key, and a predetermined signature value of the session initiating party, from each session participating party, and determining validity of the message;

(b) generating two temporary secret keys for each session participating party, two temporary public keys for each session participating party, and a signature value obtained by applying a predetermined signature function to the two temporary public keys for each session participating party;

(c) sending a message, including the temporary public keys for each session participating party and the signature value, to the session initiating party;

(d) receiving a message, including a shared key generation variable and encrypted ID information of the session initiating party, from the session initiating party;

(e) generating a session shared key using the shared key generation variable and the temporary secret keys for each session participating party; and

(f) decrypting the encrypted ID information of the session initiating party using the session shared key, and determining whether the session shared key is valid.