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Lecture notes in computer science

Black-Box Separations for Non-interactive Classical Commitments in a Quantum World

Kai-Min Chung, Yao-Ting Lin, Mohammad Mahmoody

Published Jan 1, 2023• 7 citations
Publisher
DOI
10.1007/978-3-031-30545-0_6

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Classically, it is well-known that several fundamental cryptographic primitives, including one-way functions, pseudorandom number generators, commitments, and signatures, characterize the same cryptographic world, which is known as "Minicrypt". In this paper, we investigate to what extent this picture persists in the quantum-computation classical-communication (QCCC) setting, where parties may perform quantum local computation, but communicate through only classical messages. We demonstrate that the classical Minicrypt landscape breaks down in the QCCC model by oracle separations. We construct two oracle worlds where efficiently verifiable one-way puzzles (EV-OWPuzz) exist. By a known equivalence, QCCC one-time signatures also exist in both worlds. In the first, one-way functions do not exist, even if we allow quantum pseudodeterministic evaluation. In the second, QCCC bit commitments do not exist. Thus, the classical Minicrypt reductions from signatures to one-way functions and bit commitments have no fully black-box counterparts in the QCCC setting. Our proofs develop techniques for analyzing the random phase states, including a concentration theorem and an LOCC decoupling theorem. As a separate result, we establish quantum sum-binding for the NOVY protocol, settling the question of its post-quantum security. We also generalize it to a fully black-box construction of a QCCC commitment from EV-OWPuzz with nearly uniform puzzle distribution, complementing our oracle separation results.

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We construct two-message non-malleable commitments with respect to opening in the standard model, assuming only one-to-one one-way functions. Our protocol consists of two unidirectional messages by the committer (with no message from the receiver), and is secure against all polynomial-time adversaries in the standard synchronous setting. Pass (TCC 2013) proved that any commitment scheme with non-malleability with respect to commitment, using only 2 rounds of communication, cannot be proved secure via a black-box reduction to any "standard" intractability assumption. We extend this by showing a similar impossibility result for commitments with non-malleability with respect to opening, another standard notion of non-malleability for commitments, for any 2-message challenge-response protocol, as well. However, somewhat surprisingly, we show that this barrier breaks down in the setting of two unidirectional messages by the committer (with no message from the receiver), for non-malleability with respect to opening.°Our protocol makes only black-box use of any non-interactive statistically binding commitment scheme. Such a scheme can be based on any one-to-one one-way function.°Our techniques depart significantly from the commit-challenge-response structure followed by nearly all prior works on non-malleable protocols in the standard model. Our methods are combinatorial in nature.°Our protocol resolves the round complexity of commitments with non-malleability with respect to opening via natural (non-embedding) black-box security reductions. We show that completely non-interactive non-malleable commitments w.r.t. opening cannot be proved secure via most natural black-box reductions. This result extends to also rule out bi-directional two-message non-malleable commitments w.r.t. opening in the synchronous or asynchronous setting.°Our protocol, together with our impossibility result, also resolves the round complexity of block-wise non-malleable codes (Chandran et al) w.r.t. natural black-box reductions.

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Non-malleable commitment is one of the most fundamental cryptographic primitives in that it is often used as a basic building block in modern cryptography. Briefly, a commitment scheme allows a sender to commit to a value while keeping the value secret from the receiver. In addition, when the commitment is opened in a later stage, the scheme guarantees that the sender can reveal only the unique value being committed to in the previous stage. A commitment scheme is said to be non-malleable if no adversary can succeed in committing to a related massage m', after seeing a commitment of a message m. In this dissertation, we study the construction of non-malleable commitments and some of their applications.A black-box construction of non-malleable commitment is presented in the first part of this dissertation. Our protocol requires only a constant number of rounds and satisfies the standard notion of non-malleability w.r.t. commitment. Our technique is based on ideas from the ``zero-knowledge from secure multi-party computation'' paradigm by Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2007). Furthermore, our construction only uses one-way functions as a black-box and thus does not depend on the actual implementation details of the functions. Prior to our result, under the standard notion of security, no black-box construction of constant-round non-malleable commitment was known. Hence, our main result closes the gap between black-box and non-black-box constructions for the problem of non-malleable commitment.In the second part of this dissertation, we show that our technique can be applied to multiple applications. Specifically, we extend our work to obtain a constant-round concurrent non-malleable commitment, a constant-round multi-party parallel coin tossing, and a non-malleable statistically hiding commitment (according to the notion of non-malleability w.r.t. opening.) Additionally, all results mentioned above are based only on a black-box use of one-way functions.

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Quantum commitments from complexity assumptions

André Chailloux, Iordanis Kerenidis, Bill Rosgen

Computational Complexity•Oct 29, 2015•4 citations
Classically, it is well-known that several fundamental cryptographic primitives, including one-way functions, pseudorandom number generators, commitments, and signatures, characterize the same cryptographic world, which is known as "Minicrypt". In this paper, we investigate to what extent this picture persists in the quantum-computation classical-communication (QCCC) setting, where parties may perform quantum local computation, but communicate through only classical messages. We demonstrate that the classical Minicrypt landscape breaks down in the QCCC model by oracle separations. We construct two oracle worlds where efficiently verifiable one-way puzzles (EV-OWPuzz) exist. By a known equivalence, QCCC one-time signatures also exist in both worlds. In the first, one-way functions do not exist, even if we allow quantum pseudodeterministic evaluation. In the second, QCCC bit commitments do not exist. Thus, the classical Minicrypt reductions from signatures to one-way functions and bit commitments have no fully black-box counterparts in the QCCC setting. Our proofs develop techniques for analyzing the random phase states, including a concentration theorem and an LOCC decoupling theorem. As a separate result, we establish quantum sum-binding for the NOVY protocol, settling the question of its post-quantum security. We also generalize it to a fully black-box construction of a QCCC commitment from EV-OWPuzz with nearly uniform puzzle distribution, complementing our oracle separation results.
We construct two-message non-malleable commitments with respect to opening in the standard model, assuming only one-to-one one-way functions. Our protocol consists of two unidirectional messages by the committer (with no message from the receiver), and is secure against all polynomial-time adversaries in the standard synchronous setting. Pass (TCC 2013) proved that any commitment scheme with non-malleability with respect to commitment, using only 2 rounds of communication, cannot be proved secure via a black-box reduction to any "standard" intractability assumption. We extend this by showing a similar impossibility result for commitments with non-malleability with respect to opening, another standard notion of non-malleability for commitments, for any 2-message challenge-response protocol, as well. However, somewhat surprisingly, we show that this barrier breaks down in the setting of two unidirectional messages by the committer (with no message from the receiver), for non-malleability with respect to opening.°Our protocol makes only black-box use of any non-interactive statistically binding commitment scheme. Such a scheme can be based on any one-to-one one-way function.°Our techniques depart significantly from the commit-challenge-response structure followed by nearly all prior works on non-malleable protocols in the standard model. Our methods are combinatorial in nature.°Our protocol resolves the round complexity of commitments with non-malleability with respect to opening via natural (non-embedding) black-box security reductions. We show that completely non-interactive non-malleable commitments w.r.t. opening cannot be proved secure via most natural black-box reductions. This result extends to also rule out bi-directional two-message non-malleable commitments w.r.t. opening in the synchronous or asynchronous setting.°Our protocol, together with our impossibility result, also resolves the round complexity of block-wise non-malleable codes (Chandran et al) w.r.t. natural black-box reductions.
Non-malleable commitment is one of the most fundamental cryptographic primitives in that it is often used as a basic building block in modern cryptography. Briefly, a commitment scheme allows a sender to commit to a value while keeping the value secret from the receiver. In addition, when the commitment is opened in a later stage, the scheme guarantees that the sender can reveal only the unique value being committed to in the previous stage. A commitment scheme is said to be non-malleable if no adversary can succeed in committing to a related massage m', after seeing a commitment of a message m. In this dissertation, we study the construction of non-malleable commitments and some of their applications.A black-box construction of non-malleable commitment is presented in the first part of this dissertation. Our protocol requires only a constant number of rounds and satisfies the standard notion of non-malleability w.r.t. commitment. Our technique is based on ideas from the ``zero-knowledge from secure multi-party computation'' paradigm by Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2007). Furthermore, our construction only uses one-way functions as a black-box and thus does not depend on the actual implementation details of the functions. Prior to our result, under the standard notion of security, no black-box construction of constant-round non-malleable commitment was known. Hence, our main result closes the gap between black-box and non-black-box constructions for the problem of non-malleable commitment.In the second part of this dissertation, we show that our technique can be applied to multiple applications. Specifically, we extend our work to obtain a constant-round concurrent non-malleable commitment, a constant-round multi-party parallel coin tossing, and a non-malleable statistically hiding commitment (according to the notion of non-malleability w.r.t. opening.) Additionally, all results mentioned above are based only on a black-box use of one-way functions.