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 for ciphertext messages, comprising:
receiving from a sender a public key of a key pair that is used for a single message, a ciphertext message that was encrypted using the key pair, and a second value s of a digital signature that was generated using the key pair and that comprises a first value r and the second value s;
decrypting the ciphertext message into a plaintext message;
calculating the first value r of the digital signature using the plaintext message and the public key; and
validating the digital signature based on the calculated first value r and the received second value s.
2. The public-key decryption process of claim 1 , wherein the ciphertext message was encrypted utilizing an El Gamal encryption scheme.
3. The public-key decryption process of claim 1 , wherein the step of validating the digital signature comprises hashing the plaintext message.
4. The public-key decryption process of claim 1 , wherein the key pair was produced by performing steps comprising:
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 , wherein the decrypting step comprises:
generating a secret key K=bX; and
decrypting the ciphertext message using the secret key K to generate a 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 , wherein the decrypting step comprises:
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;
wherein decrypting the 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 a public key X of a key pair that is used for a single message, a ciphertext message that was encrypted using the key pair, and a second value s of a digital signature that was generated using the key pair and that comprises a first value r and the second value s;
the communication device is configured to decrypt the ciphertext message into a plaintext message;
the communication device is configured to calculate the first value r of the digital signature using the plaintext message and the public key; and
the communication device is configured to validate the digital signature based on 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 the plaintext message 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 the cybertext 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 the 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 a public key X of a key pair that is used for a single message, a ciphertext message that was encrypted using the key pair, and a second value s of a digital signature that was generated using the key pair and that comprises a first value r and the second value s;
decrypting the ciphertext message into a plaintext message;
calculating the first value r of the digital signature using the plaintext message and the public key; and
validating the digital signature based on 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 the plaintext message when validating the digital signature.
17. 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 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 15 , 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.