Information Security and Cryptography Research Group

Quantum Cryptography with Finite Resources

Valerio Scarani and Renato Renner

Available on, Aug 2007.

The security of a key generated from finite resources is always finite. We present a lower bound for the security of finite keys in quantum cryptography, with respect to a definition of security thatis composable and has an operational meaning – two crucial requirements for practical applications. For single-qubit implementations of the Bennett-Brassard 1984 and the six-statesprotocols, the secret key rate becomes positive when at least N 10^5 signals are exchanged and processed, and reaches the asymptotic value only for N 10^{15}.

BibTeX Citation

    author       = {Valerio Scarani and Renato Renner},
    title        = {Quantum Cryptography with Finite Resources},
    year         = {2007},
    month        = {8},
    howpublished = {Available on},

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