Method to reduce the latency of ECDSA signature generation using precomputation
In order to reduce latency of elliptical curve digital signature generation a portion of the digital signature is pre-calculated before receipt of the message hash using an unmodified ECDSA computing engine. After the message hash is received, the digital signature is completed without using the ECDSA computing engine. Applications include generating digital signatures for the safety messages in Intelligent Transport Systems.
1. A method to reduce the latency of elliptical curve digital signature generation using pre-computation comprising:
pre-computing an incomplete elliptical curve digital signature using a security-hardened ECDSA computing engine, wherein the incomplete elliptical curve digital signature is pre-computed using a dummy message hash;
receiving, in a cryptographic coprocessor, a message hash outside of the security-hardened ECDSA computing engine; and
completing, in the cryptographic coprocessor, computation of an elliptical curve digital signature outside of the security-hardened ECDSA computing engine after the receipt of the message hash by using the incomplete elliptical curve digital signature as input.
2. The method of claim 1 , wherein pre-computing the incomplete elliptical curve digital signature further comprises:
computing r=x mod n, where x is a first coordinate of a curve point, n an integer is an order of G, and G is an elliptic curve base point.
3. The method of claim 2 , wherein the order of G means that n*G=0, wherein 0 is an identity element and * denotes elliptic curve point multiplication by a scalar.
4. The method of claim 1 , wherein an inverse of a private key integer is pre-computed.
5. The method of claim 1 , wherein a dummy message hash value of zero is used as the dummy message hash as an input to the security-hardened ECDSA computing engine for pre-computing the incomplete elliptical curve digital signature.
6. An Intelligent Transportation System using the method of claim 5 to generate the elliptical curve digital signature.
7. The system of claim 6 , wherein an inverse of a private key integer is pre-computed each time a pseudo-identity related to the private key integer is changed.
8. The method of claim 1 , wherein completing computation of the elliptical curve digital signature in the cryptographic coprocessor outside the security-hardened ECDSA computing engine uses blinding.
9. An Intelligent Transportation System using the method of claim 1 to generate the elliptical curve digital signature.
10. The Intelligent Transportation System of claim 9 , wherein the elliptical curve digital signature is used to sign a safety message.
11. The method of claim 1 , further comprising:
computing a modular inverse to complete the computation of the elliptical curve digital signature.
12. The method of claim 11 , further comprising:
computing the modular inverse in the cryptographic coprocessor.