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...ever, the security of classical bit commitment schemes relies on unproved assumptions on computational complexity, while unconditionally secure quantum bit commitment has been proved to be impossible =-=[29]-=-, [30]. In this section, we use the main idea of the bit hiding scheme in Section III to construct a conditionally secure bit commitment scheme in the following setting. The commitment is shared betwe...

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...ange between two honest players. However, in the case of two mutually distrusting parties, we are not so fortunate: even with quantum communication, unconditionally secure BC and OT remain impossible =-=[15, 17]-=-. There are, however, several scenarios where these impossibility results do not apply, namely: • if the computing power of players is bounded, • if the communication is noisy, • if the adversary is u...

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... general theorem seems to be of independent interest. A classical version of the theorem can be found in, e.g., [9]. We also use another primitive derived from the work of Lo and Chau [17] and Mayers =-=[18]-=- which combines results of Jozsa [12], and Fuchs and van de Graaf [11]. Consider two bi-partite pure states such that one party sharing the states cannot locally distinguish between the two states wit...

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...ey distribution[5], many attempts have been made to exploit the unique properties of quantum systems to provide new cryptographic primitives. A great surprise was the failure of quantum bit commitment=-=[19, 18]-=-; subsequently, less powerful but still interesting primitives such as quantum bit escrow[1] were introduced. Looking beyond cryptography, many more new quantum protocols have been discovered, such as...

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...nt one. Without any kind of computational assumptions and assuming noiseless communications, commitment schemes are impossible (see e.g. [15]; the generalisation to quantum protocols is due to Mayers =-=[20]-=-). Therefore, research has mostly focused on schemes were the receiver is computationally bounded (computationally concealing schemes) or schemes were the sender is computationally bounded (computatio...

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...]. But in a scenario with only two players, neither primitive can be implemented with unconditional security based only on standard, error free communication. Even quantum communication does not help =-=[14, 13]-=-. However, Crépeau and Kilian have shown that both primitives can be implemented based on a binary symmetric channel (BSC) [5]. A BSC is a channel for transmitting single bits, and for every bit tran...

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...y from scratch, i.e., between parties connected by a noiseless channel; in fact, not even if this is a quantum channel over which the parties can exchange not only “classical” bits but quantum states =-=[14]-=-. However, if some additional weak and realistic primitives are available such as noisy channels and noisy correlations, then unconditional security can be often achieved [6], [5], [7], [12], [21], [2...