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Both of these results are provably impossible to achieve in the standard quantum interactive model. A quantum bit-commitment that is both statistically hiding and statistically binding is known to be impossible in itself, even without perfect hiding. See [May97, LC98] for impos- sibility results regarding commitments and [GKR08, BGS13] for impossibility results on ideal oblivious transfer, also known as one-time memories. amas 2 aaa aaa aaa RI le It can easily be seen that the scheme is perfectly secure against malicious senders, as no data is sent from the receiver to the sender. Security against malicious receivers is more intricate and is detailed in [Sch07]. We provide in Appendix A an alternative proof to that of [Sch07] regarding security against malicious receivers based on the monogamy of entanglement property [TFKW13]. For simplicity’s sake, we prove a weaker security notion than that in [Sch07]. However, by altering the proof’s last stages, the same result as in [Sch07] can be achieved (see Remark 5).

Table 1 Both of these results are provably impossible to achieve in the standard quantum interactive model. A quantum bit-commitment that is both statistically hiding and statistically binding is known to be impossible in itself, even without perfect hiding. See [May97, LC98] for impos- sibility results regarding commitments and [GKR08, BGS13] for impossibility results on ideal oblivious transfer, also known as one-time memories. amas 2 aaa aaa aaa RI le It can easily be seen that the scheme is perfectly secure against malicious senders, as no data is sent from the receiver to the sender. Security against malicious receivers is more intricate and is detailed in [Sch07]. We provide in Appendix A an alternative proof to that of [Sch07] regarding security against malicious receivers based on the monogamy of entanglement property [TFKW13]. For simplicity’s sake, we prove a weaker security notion than that in [Sch07]. However, by altering the proof’s last stages, the same result as in [Sch07] can be achieved (see Remark 5).

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The perfectness is due to the perfect hiding of AmCom. Such a result is not known in th standard interactive classical or quantum models, even if statistical zero-knowledge proofs ar considered instead. Interestingly, the corresponding complexity classes of decision problem: or which there exists statistical zero-knowledge proofs possess some interesting qualities i she standard classic or quantum interactive models. Amongst those closure under complemen {Oka96, Wat02]) and the equivalence of honest and dishonest verification [GSV98, Wat09] which additionally holds even in the computational setting ([Vad06, Kob08]). We find it in ‘eresting to ponder whether analogs hold for the appropriate class in Quamnesia, either it computational, statistical, or perfect settings. A critical step appears to be finding a complet: oroblem for the appropriate classes in Quamnesia. a, ne ed ® «+ Tt ae | 1 er 11 +1 1 a op 1. 1 +> W
The perfectness is due to the perfect hiding of AmCom. Such a result is not known in th standard interactive classical or quantum models, even if statistical zero-knowledge proofs ar considered instead. Interestingly, the corresponding complexity classes of decision problem: or which there exists statistical zero-knowledge proofs possess some interesting qualities i she standard classic or quantum interactive models. Amongst those closure under complemen {Oka96, Wat02]) and the equivalence of honest and dishonest verification [GSV98, Wat09] which additionally holds even in the computational setting ([Vad06, Kob08]). We find it in ‘eresting to ponder whether analogs hold for the appropriate class in Quamnesia, either it computational, statistical, or perfect settings. A critical step appears to be finding a complet: oroblem for the appropriate classes in Quamnesia. a, ne ed ® «+ Tt ae | 1 er 11 +1 1 a op 1. 1 +> W
“Strong coin-flipping contrasts with weak coin-flipping by the goals of the parties: in weak coin-flipping, Alice hopes to flip 0, and Bob hopes to flip 1; hence Bob being able to force the result 0 with probability 3 would only be detrimental to himself, and thus would not be considered cheating; in strong coin-flipping, any bias may be beneficial to a cheating party, and hence any non-uniform distribution of the coin is considered cheating.
“Strong coin-flipping contrasts with weak coin-flipping by the goals of the parties: in weak coin-flipping, Alice hopes to flip 0, and Bob hopes to flip 1; hence Bob being able to force the result 0 with probability 3 would only be detrimental to himself, and thus would not be considered cheating; in strong coin-flipping, any bias may be beneficial to a cheating party, and hence any non-uniform distribution of the coin is considered cheating.
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