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I know, that quantum computers can theoretically break the discrete logarithm problem using the shor algorithm. The problem with quantum computers is not the time, but the space ( the needed qubits ). My question is: Can elliptic curve cryptographie be adjusted so that they are secure against quantum computers? ( e.g. longer key length )

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    $\begingroup$ Does this answer to your question How effective is quantum computing against elliptic curve cryptography? $\endgroup$
    – kelalaka
    Commented Jul 31, 2020 at 11:00
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    $\begingroup$ Related to your question: Supersingular isogeny key exchange. $\endgroup$ Commented Jul 31, 2020 at 11:59
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    $\begingroup$ "The problem with quantum computers is not the time, but the space ( the needed qubits )" - actually, as we don't have a real quantum computer (a cryptographically relevant one) in front of us, we don't know what would be its most critical constraints - it may be the number of qubits, it may be a bound on the circuit depth, it may be limitations on moving the qubits around... $\endgroup$
    – poncho
    Commented Jul 31, 2020 at 12:50
  • $\begingroup$ Main problem with Quantum Computers has been the measuring of the Qbit-state, typically 30% failure for a set of 14Qbits and this grows exponentially with the set size. Guess, for a long time, security will rely on the dimension of combinatorial problems, meaning your question is less ECC specific. Guess finally we'll have a performance race ECC vs RSA with long keys and AES certainly dead. $\endgroup$ Commented Jan 5, 2022 at 19:13

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