I want to know the execution times of the following cryptographic primitives involved in ECC:
1. ECC point addition
2. ECC point multiplication
3. ECDSA signing time
4. ECDSA signature verification time
Can anyone please help me with this.
1) It depends by your architecture and your CPU.
2) It depends by the elliptic curve that you are considering, i.e. secp160r1, secp192r1, ecc. (and the respective Koblitz version).
3) It depends if you are considering pre-computations or not.
4) It depends if you are estimating these costs in C or Python or another generic language. By the way, from my experience you should work in C to estimate how much time requires an ECC operation. As a standard library to make these experiments, I can suggest you OpenSSL.
5) The best option is to measure the time and the energy consumption by adopting an oscilloscope.
6) Further you need to repeat the tests (i.e. 10,000 times) and compute the mean + interval confidence at 95%.
7) An example here (Section VI A): Article LiKe: Lightweight Certificateless Key Agreement for Secure I...
Lets say I know the ECC point addition and multiplication times. Can I approximate the ECDSA signing and verification times using it?
More or less yes. In details
- An EC multiplication require more times compared to an EC addition.
- Secondly, you can approximate the ECDSA algorithm to: 1 EC_MUL, but you are missing the cost of an hashing function (negligible), the cost of a module operation (x2), the cost to invert the random integer (kept secret). This is to sign.
- In order to verify the signature, please try to see how the verification algorithm works and make some assumption(s) --> https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm
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