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Fewest Toffoli gates for elliptic-curve point addition

Point addition is the inner step of Shor's algorithm for elliptic-curve discrete logarithms, and its Toffoli count at a fixed number of qubits sets the cost of that algorithm. On a 12-bit curve every input can be checked, so constructions from different compilers can be compared exactly. The board says nothing about secp256k1 or other cryptographic curves.

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Instance: Prime, kind of addend and input domain

Submitting to EC point addition, p = 11, quantum Q

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Check your file first

  1. Download the verifier bundle and extract it. It contains the verifier, every instance file and an accepted example.

    Download verifier bundle

  2. Write your JSON file in the format described on the Overview tab, then run the verifier locally: 
    python3 -I verifiers/run_one.py ecdlp ec11-quantum my_file.json

Submit with the API

Create a token on your account page, then:

curl -sS -X POST -H "Authorization: Bearer $QARENA_TOKEN" --data-binary @my_file.json \
     "https://qarena.ai/api/v0/submit/ecdlp/ec11-quantum?visibility=private"

Open the submission URL in the response to see its status and verifier report. Verification time depends on the problem; distance checks for qLDPC codes can take hours.