TY - GEN
T1 - Noisy Feedback and Loss Unlimited Private Communication
AU - Ding, Dawei
AU - Guha, Saikat
N1 - Funding Information:
Lastly, it is worth looking at the closely related communication models of two way private communication, secret key agreement, and quantum key distribution. If we make the same alteration, that is, introduce noise in the classical feedback in the initial round, Bob can simply send an arbitrarily long locally generated random bit string to Alice during that round. Alice will then receive this key noiselessly, while Eve will only receive a noisy copy whose mutual information with the key is finite since the capacity of the noisy feedback channel is finite. Hence, in these models the infinite difference in capacities trivially leads to an infinite rate. This again shows the dependence of the rates to the model considered and suggests that in general we should more seriously address blatant unphysical features in the communication model. Acknowledgements. We would like to thank Patrick Hay-den and Tsachy Weissman for valuable discussions and feedback. SG was supported by the CONQUEST program funded by the ONR under Raytheon prime contract # N00014-16-C-2069. DD would like to thank God for all of His provisions.
Publisher Copyright:
© 2018 IEEE.
PY - 2018/8/15
Y1 - 2018/8/15
N2 - Cryptographic protocols often involve the assistance of public side channels to which all parties have perfectly noiseless access. For instance, in the BB84 quantum key distribution protocol, the side channel is used to share the bases in which Alice and Bob encoded or measured their qubits. In this paper, we find that in the case of continuous variable communication, by slightly altering this model such that Eve's copy of the initial round of feedback is corrupted by an iota of noise while keeping Alice's copies noiseless, the capacity can be increased dramatically. Specifically, it is known that the private capacity with noiseless feedback for a pure-loss bosonic channel is at most -\log(1-\eta) bits per mode, where \eta is the transmissivity, in the limit of infinite input photon number. This is a very pessimistic result as there is a finite rate limit even with an arbitrarily large number of input photons. We refer to this as a loss limited rate. However, in our altered model we find that we can achieve a rate of (1/2) \log(1+4\eta N-{S}) bits per mode with weak security, where N-{S} is the input photon number. This rate diverges with N-{S}, in sharp contrast to the result for the original model. This suggests that physical considerations behind the eavesdropping model should be taken more seriously, as they can create strong dependencies of the achievable rates on the model. For by a seemingly inconsequential weakening of Eve, we obtain a loss-unlimited rate. Our protocol also works verbatim for arbitrary i.i \mathrm{d}, noise (not even necessarily Gaussian) injected by Eve in every round, and even if Eve is given access to copies of the initial transmission and noise. The error probability of the protocol decays super-exponentially with the blocklength.
AB - Cryptographic protocols often involve the assistance of public side channels to which all parties have perfectly noiseless access. For instance, in the BB84 quantum key distribution protocol, the side channel is used to share the bases in which Alice and Bob encoded or measured their qubits. In this paper, we find that in the case of continuous variable communication, by slightly altering this model such that Eve's copy of the initial round of feedback is corrupted by an iota of noise while keeping Alice's copies noiseless, the capacity can be increased dramatically. Specifically, it is known that the private capacity with noiseless feedback for a pure-loss bosonic channel is at most -\log(1-\eta) bits per mode, where \eta is the transmissivity, in the limit of infinite input photon number. This is a very pessimistic result as there is a finite rate limit even with an arbitrarily large number of input photons. We refer to this as a loss limited rate. However, in our altered model we find that we can achieve a rate of (1/2) \log(1+4\eta N-{S}) bits per mode with weak security, where N-{S} is the input photon number. This rate diverges with N-{S}, in sharp contrast to the result for the original model. This suggests that physical considerations behind the eavesdropping model should be taken more seriously, as they can create strong dependencies of the achievable rates on the model. For by a seemingly inconsequential weakening of Eve, we obtain a loss-unlimited rate. Our protocol also works verbatim for arbitrary i.i \mathrm{d}, noise (not even necessarily Gaussian) injected by Eve in every round, and even if Eve is given access to copies of the initial transmission and noise. The error probability of the protocol decays super-exponentially with the blocklength.
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U2 - 10.1109/ISIT.2018.8437575
DO - 10.1109/ISIT.2018.8437575
M3 - Conference contribution
AN - SCOPUS:85052486379
SN - 9781538647806
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 586
EP - 590
BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018
Y2 - 17 June 2018 through 22 June 2018
ER -