Public key encryption with digital signature scheme
View Patent ↗An improved encryption and digital signature system and method in accordance with the invention reuses an encryption ephemeral key pair from an encryption process in a digital signature process. The reuse of the encryption ephemeral key pair in the digital signature process advantageously results in reduced byte size of the digital signature and reduction of costly computation overhead. In a preferred embodiment, the invention is based on the El Gamal encryption scheme and the Nyberg-Rueppel signature scheme. The present invention is particularly useful for operation in conjunction with small communication devices having limited processing and storage, wherein such devices may communicate via bandwidth sensitive RF links.
1. A public-key decryption process, comprising:
receiving from a sender (1) a public key of a key pair that is used for a single message, and (2) a second value s of a digital signature that was generated using the key pair, the digital signature comprising a first value r and the second value s;
calculating the first value r of the digital signature using the public key; and
validating the digital signature based upon the calculated first value r and the received second value s.
2. The public-key decryption process of claim 1 , wherein a ciphertext message that was encrypted using the key pair is also received from the sender.
3. The public-key decryption process of claim 2 , wherein validating the digital signature comprises hashing a plaintext message that is encrypted within the ciphertext message.
4. The public-key decryption process of claim 1 , wherein the key pair was produced by:
generating a private key x; and
calculating the public key X=xG in a finite cyclic group having G as a generator.
5. The public-key decryption process of claim 4 , the process comprising decrypting a ciphertext message received from the sender into a plaintext message by:
generating a secret key K=bX; and
decrypting the ciphertext message using the secret key K to generate the plaintext message.
6. The public-key decryption process of claim 5 , wherein the sender used the private key x as a signature private key and used the public key X as a signature public key to generate the digital signature.
7. The public-key decryption process of claim 4 , the process comprising decrypting a ciphertext message received from the sender into a plaintext message by:
generating a secret key K by calculating one of: bX, bxG, xbG, and xB; and
decrypting the ciphertext message using the generated secret key K.
8. The public-key decryption process of claim 1 implemented in a wireless communication system,
wherein at least a two stage public-key decryption process is used,
wherein a first stage includes key establishment and the second stage includes decryption, and
wherein decrypting a plaintext message and validating the digital signature are performed during the second stage.
9. The public-key decryption process of claim 1 , further comprising:
at a sender,
generating a sender private key a; and
calculating a sender public key A=aG, where G is a generator;
and at a receiver,
generating a receiver private key b; and
calculating a receiver public key B=bG,
wherein the sender obtains an authentic copy of the receiver public key B and the receiver obtains an authentic copy of the sender public key A.
10. A communication device, comprising:
a computer-readable memory encoded with software instructions; and wherein:
the communication device is configured to receive from a sender (1) a public key of a key pair that is used for a single message, and (2) a second value s of a digital signature that was generated using the key pair, the digital signature comprising a first value r and the second value s;
the communication device is configured to calculate the first value r of the digital signature using the public key; and
the communication device is configured to validate the digital signature based upon the calculated first value r and the received second value s.
11. The communication device of claim 10 , wherein the communication device is further configured to hash a plaintext message encoded within a ciphertext received from the sender when validating the digital signature.
12. The communication device of claim 10 , wherein the communication device is further configured to generate a secret key K=bX where b is a receiver private key; and wherein the communication device is further configured to decrypt a ciphertext message using the secret key K.
13. The communication device of claim 10 , wherein the communication device is further configured to generate a secret key K by calculating one of: bX, bxG, xbG, and xB where b is a receiver private key, B is a receiver public key, x is a private key of the key pair that is used for a single message and G is a generator; and wherein the communication device is further configured to decrypt a ciphertext message using the secret key K.
14. The communication device of claim 10 , wherein the communication device is further configured to:
generate a receiver private key b;
calculate a receiver public key B=bG, where G is a generator; and
obtain an authentic copy of the sender public key A.
15. A wireless device for decrypting data, comprising:
a data processor;
a computer-readable memory encoded with instructions for commanding the data processor to execute steps including:
receiving from a sender (1) a public key of a key pair that is used for a single message, and (2) a second value s of a digital signature that was generated using the key pair, the digital signature comprising a first value r and the second value s;
calculating the first value r of the digital signature using the public key; and
validating the digital signature based upon the calculated first value r and the received second value s.
16. The wireless device of claim 15 , wherein the computer-readable memory is further encoded with instructions for commanding the data processor to execute steps including hashing a plaintext message encoded within a ciphertext message received from the sender when validating the digital signature.
17. The wireless device of claim 16 , wherein the computer-readable memory is further encoded with instructions for commanding the data processor to execute steps including:
generating a secret key K=bX where b is a receiver private key; and
decrypting the ciphertext message using the secret key K.
18. The wireless device of claim 16 , wherein the computer-readable memory is further encoded with instructions for commanding the data processor to execute steps including:
generating a secret key K by calculating one of: bX, bxG, xbG, and xB where b is a receiver private key, B is a receiver public key, x is a private key of the key pair that is used for a single message and G is a generator; and
decrypting the ciphertext message using the secret key K.
19. The wireless device of claim 15 , wherein the computer-readable memory is further encoded with instructions for commanding the data processor to execute steps including:
generating a receiver private key b;
calculating a receiver public key B=bG, where G is a generator; and
obtaining an authentic copy of the sender public key A.