We present a non-malleable commitment scheme that retains its security properties even when concurrently executed a polynomial number of times. That is, a man-in-the-middle adversary who is simultaneously participating in multiple concurrent commitment phases of our scheme, both as a sender and as a receiver cannot make the values he commits to depend on the values he receives commitments to. Our result is achieved without assuming an a-priori bound on the number of executions and without relying on any set-up assumptions. Our construction relies on the existence of standard collision resistant hash functions and only requires a constant number of communication rounds.
We present a non-malleable commitment scheme that retains its security properties even when concurrently executed a polynomial number of times. That is, a man-in-the-middle adversary who is simultaneously participating in multiple concurrent commitment phases of our scheme, both as a sender and as a receiver cannot make the values he commits to depend on the values he receives commitments to. Our result is achieved without assuming an a-priori bound on the number of executions and without relying on any set-up assumptions. Our construction relies on the existence of standard collision resistant hash functions and only requires a constant number of communication rounds.
We present a nonmalleable commitment scheme that retains its security properties even when concurrently executed a polynomial number of times. That is, a man-in-the-middle adversary who is simultaneously participating in multiple concurrent commitment phases of our scheme, both as a sender and as a receiver, cannot make the values to which he commits depend on the values to which he receives commitments. Our result is achieved without assuming an a priori bound on the number of executions and without relying on any setup assumptions. Our construction relies on the existence of standard claw-free permutations and requires only a constant number of communication rounds.
Commitment schemes are fundamental building blocks in cryptography, and have wide applications in constructing various protocols. Non-malleable commitment considers concurrent executions of a commitment scheme against a man-in-the-middle adversary. In this paper, we investigate non-malleability of statistically hiding commitment schemes, and present the first concurrent non-malleable statistically hiding commitment scheme. Our protocol admits black-box simulation, and relies on the robust (stand-alone) non-malleable commitment and specially designed witness indistinguishable proofs to achieve concurrent non-malleability. Based on the one-way function assumption, the commit phase of our protocol needs polynomial rounds, and the decommit phase needs super-logarithmic rounds.
Non-malleable commitments are a fundamental cryptographic tool for preventing against (concurrent) man-in-the-middle attacks. Since their invention by Dolev, Dwork, and Naor in 1991, the round-complexity of non-malleable commitments has been extensively studied, leading up to constant-round concurrent non-malleable commitments based only on one-way functions, and even 3-round concurrent non-malleable commitments based on subexponential one-way functions. But constructions of two-round, or non-interactive, nonmalleable commitments have so far remained elusive; the only known construction relied on a strong and non-falsifiable assumption with a non-malleability flavor. Additionally, a recent result by Pass shows the impossibility of basing two-round non-malleable commitments on falsifiable assumptions using a polynomial-time black-box security reduction. In this work, we show how to overcome this impossibility, using super-polynomial-time hardness assumptions. Our main result demonstrates the existence of a two-round concurrent non-malleable commitment based on subexponential “standard-type” assumptions-notably, assuming the existence of the following primitives (all with subexponential security): (1) non-interactive commitments, (2) ZAPs (i.e., 2-round witness indistinguishable proofs), (3) collision-resistant hash functions, and (4) a “weak” time-lock puzzle. Primitives (1),(2),(3) can be based on e.g., the discrete log assumption and the RSA assumption. Time-lock puzzles-puzzles that can be solved by “brute-force” in time 2t, but cannot be solved significantly faster even using parallel computers-were proposed by Rivest, Shamir, and Wagner in 1996, and have been quite extensively studied since; the most popular instantiation relies on the assumption that 2t repeated squarings mod N = pq require “roughly” 2t parallel time. Our notion of a “weak” time-lock puzzle, requires only that the puzzle cannot be solved in parallel time 2tϵ(and thus we only need to rely on the relatively mild assumption that there are no huge improvements in the parallel complexity of repeated squaring algorithms). We additionally show that if replacing assumption (2) for a non-interactive witness indistinguishable proof (NIWI), and (3) for a uniform collision-resistant hash function, then a non-interactive (i.e., one-message) version of our protocol satisfies concurrent non-malleability w.r.t. uniform attackers.
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.
Non-malleable commitments are a fundamental cryptographic tool for preventing (concurrent) man-in-the-middle attacks. Since their invention by Dolev, Dwork, and Naor in 1991, their round-complexity has been extensively studied, leading up to constant-round protocols based on one-way functions (OWFs), and three-round protocols based on sub-exponential OWFs, and standard polynomial-time hardness assumptions such as decisional Diffie--Hellman (DDH) and ZAPs (i.e., two-round witness-indistinguishable proofs). But constructions of two-round, or non-interactive, non-malleable commitments have so far remained elusive; the only known construction relied on a strong and non-falsifiable assumption with a non-malleability flavor. Additionally, a recent result by Pass shows the impossibility of basing two-round non-malleable commitments on falsifiable assumptions using a polynomial-time black-box security reduction. In this work, we show how to overcome this impossibility using super-polynomial-time hardness assumptions. Our main result demonstrates the existence of two-round concurrent non-malleable commitments based on the following four primitives (all with sub-exponential security): (1) non-interactive commitments, (2) ZAPs (i.e., 2-round witness indistinguishable proofs), (3) collision-resistant hash functions, and (4) a “weak” time-lock puzzle. Primitives (1), (2), and (3) can be based on, e.g., the discrete log and the RSA assumption. Time-lock puzzles---puzzles that can be solved by “brute-force” in time 2t, but cannot be solved significantly faster even using parallel computers---were proposed by Rivest, Shamir, and Wagner in 1996 and have been extensively studied since. We additionally obtain a non-interactive (i.e., one-message) version of our protocol satisfying concurrent non-malleability w.r.t. uniform attackers and show that our non-malleable commitments satisfy an even stronger notion of chosen commitment attack security.
We show unconditionally that the existence of commitment schemes implies the existence of constant-round non-malleable commitments; earlier protocols required additional assumptions such as collision resistant hash functions or subexponential one-way functions. Our protocol also satisfies the stronger notions of concurrent non-malleability and robustness. As a corollary, we establish that constant-round non-malleable zero-knowledge arguments for NP can be based on one-way functions and constant-round secure multi-party computation can be based on enhanced trapdoor permutations; also here, earlier protocols additionally required either collision-resistant hash functions or subexponential one-way functions.