Method for a pseudonymous key-agreement between a portable data carrier and a terminal
A pseudonymous Diffie-Hellman protocol is provided by means of a combination of the CA protocol with the RI protocol. According to the invention the determining of the pseudonym from the RI protocol and the forming of the secure communication channel from the CA protocol occur substantially in parallel. According to the invention there is likewise employed a group key for the CA part of the protocol according to the invention. Due to the configuration of the protocol according to the invention it is not possible, in contrast to the known protocols, for an attacker who should succeed in establishing the group key of a portable data carrier according to the invention, to generate the pseudonym of another user.
1. A method for pseudonymously establishing a key Z between a data carrier and a terminal device comprising:
obtaining, on the terminal device, a base element J and two group elements G 1 and G 2 , wherein a discrete logarithm of G 2 to a base G 1 is u;
obtaining, on the portable data carrier, a public key PKC and secrets s and t, wherein a public key PKC is a discrete-logarithm representation formed from the secrets s and t and the two group elements G 1 and G 2 ;
receiving, by the portable data carrier, the base element J and a first derived base element H 1 and a second derived base element H 2 from the terminal device, wherein the first derived base element H 1 is derived from the base element J and the group element G 1 using a first random number r 1 and a second random number r 2 , and the second derived base element H 2 is derived from the group element G 2 using the first random number r 1 and the second random number r 2 ;
computing, by the portable data carrier, a pseudonym K using the base element J transferred from the terminal device and the secret s;
sending, by the portable data carrier, the public key PKC and the pseudonym K to the terminal device; and
computing, by the portable data carrier, a common secret Z using the derived base elements H 1 and H 2 and the secrets s and t, wherein the common secret Z is employed as the key Z between the portable data carrier and the terminal device, the key Z facilitating a pseudonymous authentication between the portable data carrier and the terminal device having increased security.
2. The method according to claim 1 , wherein the common secret Z is computed by computing Z=H 1 *s+H 2 *t.
3. The method according to claim 1 , wherein the first derived base element H 1 is derived by computing H 1 =(G 1 *r 1 +J)*r 2 , and the second derived base element H 2 is derived by computing H 2 =G 2 *r 1 *r 2 .
4. The method according to claim 1 , wherein the pseudonym K is computed by computing K=J*s.
5. The method according to claim 4 , wherein an obfuscated pseudonym K′ is computed by the portable data carrier and sent to the terminal device.
6. The method according to claim 5 , wherein for the obfuscated pseudonym K′ it holds that K′ =K*r 3 , wherein r 3 is a random number.
7. A method for pseudonymously establishing a key Z between a portable data carrier and a terminal device comprising:
obtaining, on the terminal device, a base element J and two group elements G 1 and G 2 , wherein a discrete logarithm of G 2 to a base G 1 is u;
obtaining, on the portable data carrier, a public key PKC and secrets s and t, wherein a public key PKC is a discrete-logarithm representation formed from the secrets s and t and the two group elements G 1 and G 2 ;
generating, by the terminal device, a first random number r 1 and a second random number r 2 ;
deriving, by the terminal device, a first derived base element H 1 and a second derived base element H 2 , wherein the first derived base element H 1 is derived from the base element J and the group element G 1 using the first random number r 1 and the second random number r 2 , and the second derived base element H 2 is derived from the group element G 2 using the random number r 1 and the second random number r 2 ;
sending, by the terminal device, the base element J, the first derived base element H 1 and the second derived base element H 2 to the portable data carrier;
receiving, by the terminal device, the public key PKC and a pseudonym K of the portable data carrier, wherein the pseudonym K is formed from the base element J and the secret s; and
computing, by the terminal device, a common secret Z using the public key PKC, the first random number r 1 , the pseudonym K and the second random number r 2 , wherein the common secret Z is employed as the key Z between the portable data carrier and the terminal device, the key Z facilitating a pseudonymous authentication between the portable data carrier and the terminal device having increased security.
8. The method according to claim 7 , wherein the common secret Z is computed by computing Z=(PKC*r 1 +K)*r 2 .
9. The method according to claim 7 , wherein a positive list of the pseudonyms of all authentic portable data carriers with regard to the base element J is deposited on the terminal device.
10. The method according to claim 7 , wherein the first derived base element H 1 is derived by computing H 1 =(G 1 *r 1 +J)*r 2 , and the second derived base element H 2 is derived by computing H 2 =G 2 *r 1 *r 2 .
11. The method according to claim 7 , wherein the pseudonym K is computed by computing K=J*s.
12. The method according to claim 11 , wherein an obfuscated pseudonym K′ is computed by the portable data carrier and sent to the terminal device.
13. The method according to claim 12 , wherein for the obfuscated pseudonym K′ it holds that K′ =K*r 3 , wherein r 3 is a random number.
14. A portable data carrier configured for pseudonymously establishing a key Z between the portable data carrier and a terminal device comprising:
a central processing unit; and
a memory coupled to the central processing unit, the memory including program instructions stored thereon that, when executed by the central processing unit, cause the portable data carrier to:
obtain, on the terminal device, a base element J and two group elements G 1 and G 2 , wherein a discrete logarithm of G 2 to a base G 1 is u;
obtain, on the portable data carrier, a public key PKC and secrets s and t, wherein a public key PKC is a discrete-logarithm representation formed from the secrets s and t and the two group elements G 1 and G 2 ;
receive the base element J and a first derived base element H 1 and a second derived base element H 2 from the terminal device, wherein the first derived base element H 1 is derived from the base element J and the group element G 1 using a first random number r 1 and a second random number r 2 , and the second derived base element H 2 is derived from the group element G 2 using the first random number r 1 and the second random number r 2 ;
compute a pseudonym K using the base element J transferred from the terminal device and the secret s;
send the public key PKC and the pseudonym K to the terminal device; and
compute a common secret Z using the derived base elements H 1 and H 2 and the secrets s and t, wherein the common secret Z is employed as the key Z between the portable data carrier and the terminal device, the key Z facilitating a pseudonymous authentication between the portable data carrier and the terminal device having increased security.
15. The portable data carrier according to claim 14 , wherein the portable data carrier is a security document.