Implicitly certified digital signatures
Methods, systems, and computer programs for using an implicit certificate are disclosed. In some aspects, a message and an implicit certificate are accessed. The implicit certificate is associated with an entity. A modified message is generated by combining the message with a value based on the implicit certificate. A digital signature can be generated based on the modified message and transmitted to a recipient. In some aspects, a digital signature from an entity and a message to be verified based on the digital signature are accessed. An implicit certificate associated with the entity is accessed. A modified message is generated by combining the message with a value based on the implicit certificate. The message is verified based on the digital signature and the modified message.
1. A method of using an implicit certificate in a cryptography system, the method comprising:
modifying, by a first terminal, an unmodified message based on an implicit certificate, wherein the implicit certificate includes a public key reconstruction value of the first terminal, the public key reconstruction value of the first terminal is different than a public key of the first terminal, the public key of the first terminal is reconstructed using the public key reconstruction value of the first terminal and a public key of a certificate authority, and wherein the modifying comprises:
generating, by the first terminal, a hash value based on the implicit certificate; and
generating, by the first terminal, a modified message by combining the unmodified message with the hash value and the public key reconstruction value;
generating, by the first terminal, a digital signature based on the modified message; and
transmitting, by the first terminal, the digital signature to a second terminal over a data communication network.
2. The method of claim 1 , further comprising: transmitting the modified message to the second terminal.
3. The method of claim 1 , further comprising: transmitting the unmodified message to the second terminal.
4. The method of claim 1 , further comprising: receiving the implicit certificate from the certificate authority.
5. The method of claim 1 , wherein the implicit certificate is issued by a first certificate authority that is subordinate to a second certificate authority, and the modified message is generated by combining the unmodified message with at least one of:
a public key of the first certificate authority;
a public key of the second certificate authority;
an implicit certificate of the first certificate authority; or
an implicit certificate of the second certificate authority.
6. The method of claim 1 , further comprising: transmitting the implicit certificate to the second terminal.
7. A first terminal, comprising:
at least one hardware processor; and
a non-transitory computer-readable storage medium coupled to the at least one hardware processor and storing programming instructions for execution by the at least one hardware processor, wherein the programming instructions, when executed, cause the at least one hardware processor to perform operations comprising:
modifying, by the first terminal, an unmodified message based on an implicit certificate, wherein the implicit certificate includes a public key reconstruction value of the first terminal, the public key reconstruction value of the first terminal is different than a public key of the first terminal, the public key of the first terminal is reconstructed using the public key reconstruction value of the first terminal and a public key of a certificate authority, and wherein the modifying comprises:
generating, by the first terminal, a hash value based on the implicit certificate; and
generating, by the first terminal, a modified message by combining the unmodified message with the hash value and the public key reconstruction value;
generating, by the first terminal, a digital signature based on the modified message; and
transmitting, by the first terminal, the digital signature to a second terminal over a data communication network.
8. The first terminal of claim 7 , wherein the operations further comprise:
transmitting the modified message to the second terminal.
9. The first terminal of claim 7 , wherein the operations further comprise:
transmitting the unmodified message to the second terminal.
10. The first terminal of claim 7 , wherein the operations further comprise: receiving the implicit certificate from the certificate authority.
11. The first terminal of claim 7 , wherein the implicit certificate is issued by a first certificate authority that is subordinate to a second certificate authority, and the modified message is generated by combining the unmodified message with at least one of:
a public key of the first certificate authority;
a public key of the second certificate authority;
an implicit certificate of the first certificate authority; or
an implicit certificate of the second certificate authority.
12. The first terminal of claim 7 , wherein the operations further comprise:
transmitting the implicit certificate to the second terminal.
13. A non-transitory computer-readable medium storing instructions that are operable when executed by data processing apparatus to perform operations comprising:
modifying, by a first terminal, an unmodified message based on an implicit certificate, wherein the implicit certificate includes a public key reconstruction value of the first terminal, the public key reconstruction value of the first terminal is different than a public key of the first terminal, the public key of the first terminal is reconstructed using the public key reconstruction value of the first terminal and a public key of a certificate authority, and wherein the modifying comprises:
generating, by the first terminal, a hash value based on the implicit certificate; and
generating, by the first terminal, a modified message by combining the unmodified message with the hash value and the public key reconstruction value;
generating, by the first terminal, a digital signature based on the modified message; and
transmitting, by the first terminal, the digital signature to a second terminal over a data communication network.
14. The non-transitory computer-readable medium of claim 13 , wherein the operations further comprise: transmitting the modified message to the second terminal.
15. The non-transitory computer-readable medium of claim 13 , wherein the operations further comprise: transmitting the unmodified message to the second terminal.
16. The non-transitory computer-readable medium of claim 13 , wherein the operations further comprise: receiving the implicit certificate from the certificate authority.
17. The non-transitory computer-readable medium of claim 13 , wherein the implicit certificate is issued by a first certificate authority that is subordinate to a second certificate authority, and the modified message is generated by combining the unmodified message with at least one of:
a public key of the first certificate authority;
a public key of the second certificate authority;
an implicit certificate of the first certificate authority; or
an implicit certificate of the second certificate authority.
18. The non-transitory computer-readable medium of claim 13 , wherein the operations further comprise: transmitting the implicit certificate to the second terminal.