Generating digital signatures

1. A method for generating a digital signature, the method comprising:

accessing a symmetric key, wherein the symmetric key is based on an ephemeral public key, and the ephemeral public key is associated with an ephemeral private key;

generating, by a hardware processor on a computing device, a ciphertext based on the symmetric key and a first portion of a message;

obtaining an input value independent of a hash function and based on the ciphertext, wherein obtaining the input value comprises:

producing a concatenation of the ciphertext and a second portion of the message; and

applying at least one of a truncation function or a reduction function on the concatenation;

generating, by the hardware processor on the computing device, a digital signature value from the ephemeral private key, the input value, and a long term private key; and

transmitting the digital signature value, the ciphertext, and the second portion of the message from the computing device to another computing device.

2. The method of claim 1 , wherein obtaining the input value includes:

if the reduction function is applied on the concatenation, reducing the concatenation of the ciphertext and the second portion of the message modulo an integer n; or if the truncation function is applied on the concatenation, truncating the concatenation of the ciphertext and the second portion of the message to a specified length.

3. The method of claim 2 , wherein the integer n represents an order of a generator point G, the ephemeral private key is an integer k, and the ephemeral public key is an elliptic curve point R=kG.

4. The method of claim 1 , wherein generating the digital signature value includes computing s=k−de mod n, where s represents the digital signature value, k represents the ephemeral private key, d represents the long term private key associated with the entity, e represents the input value, and n represents an integer.

5. The method of claim 4 , wherein the ephemeral public key is a first elliptic curve point R=kG, and G is a generator point of order n.

6. The method of claim 1 , further comprising generating the symmetric key by evaluating a key derivation function based on the ephemeral public key.

7. A computing device comprising data processing apparatus operable to:

access a symmetric key, wherein the symmetric key is based on an ephemeral public key, and the ephemeral public key is associated with an ephemeral private key;

generate a ciphertext based on the symmetric key and a first portion of a message;

obtain an input value independent of a hash function and based on the ciphertext by:

producing a concatenation of the ciphertext and a second portion of the message; and

applying at least one of a truncation function or a reduction function on the concatenation;

generate a digital signature value from the ephemeral private key, the input value, and a long term private key; and

transmit the digital signature value, the ciphertext, and the second portion of the message from the computing device to another computing device.

8. The computing device of claim 7 , wherein obtaining the input value includes:

if the reduction function is applied on the concatenation, reducing the concatenation of the ciphertext and the second portion of the message modulo an integer n; or if the truncation function is applied on the concatenation, truncating the concatenation of the ciphertext and the second portion of the message to a specified length.

9. The computing device of claim 8 , wherein the integer n represents an order of a generator point G, the ephemeral private key is an integer k, and the ephemeral public key is an elliptic curve point R=kG.

10. A non-transitory computer-readable medium storing instructions that are operable when executed by data processing apparatus to perform operations for generating a digital signature, the operations comprising:

accessing a symmetric key, wherein the symmetric key is based on an ephemeral public key, and the ephemeral public key is associated with an ephemeral private key;

generating a ciphertext based on the symmetric key and a first portion of a message;

obtaining an input value independent of a hash function and based on the ciphertext, wherein obtaining the input value comprises:

producing a concatenation of the ciphertext and a second portion of the message; and

applying at least one of a truncation function or a reduction function on the concatenation;

generating, at a computing device, a digital signature value from the ephemeral private key, the input value, and a long term private key; and

transmitting the digital signature value, the ciphertext, and the second portion of the message from the computing device to another computing device.

11. The non-transitory computer-readable medium of claim 10 , wherein obtaining the input value includes:

if the reduction function is applied on the concatenation, reducing the concatenation of the ciphertext and the second portion of the message modulo an integer n; or if the truncation function is applied on the concatenation, truncating the concatenation of the ciphertext and the second portion of the message to a specified length.

12. The non-transitory computer-readable medium of claim 11 , wherein the integer n represents an order of a generator point G, the ephemeral private key is an integer k, and the ephemeral public key is an elliptic curve point R=kG.

13. The non-transitory computer-readable medium of claim 10 , wherein generating the digital signature value includes computing s=k−de mod n, where s represents the digital signature value, k represents the ephemeral private key, d represents the long term private key associated with the entity, e represents the input value, and n represents an integer.

14. The non-transitory computer-readable medium of claim 13 , wherein the ephemeral public key is a first elliptic curve point R=kG, and G is a generator point of order n.

15. The non-transitory computer-readable medium of claim 10 , wherein the operations comprise generating the symmetric key by evaluating a key derivation function based on the ephemeral public key.