Commitment schemes are important tools in cryptography and used as building blocks in many cryptographic protocols. We propose two commitment schemes by using Rubik’s groups. Our proposals do not lay the security on the taken-for-granted hardness of the word problem over Rubik’s groups. Instead, our first proposal is based on a symmetric encryption algorithm that is secure based on the hardness of the conjugacy search problem over Rubik’s groups, while our second proposal is based on the hardness of a newly derived problem—the functional towering conjugacy search problem over Rubik’s groups. The former is proved secure in the sense of both computational hiding and binding, while the latter is proved even secure in the sense of perfect hiding and computational binding. Furthermore, the proposed schemes have a remarkable performance advantage: a linear commitment/opening speed. We also evaluate the efficiency of the commitment schemes and show that they are considerably fast.
Commitment schemes are important tools in cryptography and used as building blocks in many cryptographic protocols. We propose two commitment schemes by using Rubik’s groups. Our proposals do not lay the security on the taken-for-granted hardness of the word problem over Rubik’s groups. Instead, our first proposal is based on a symmetric encryption algorithm that is secure based on the hardness of the conjugacy search problem over Rubik’s groups, while our second proposal is based on the hardness of a newly derived problem—the functional towering conjugacy search problem over Rubik’s groups. The former is proved secure in the sense of both computational hiding and binding, while the latter is proved even secure in the sense of perfect hiding and computational binding. Furthermore, the proposed schemes have a remarkable performance advantage: a linear commitment/opening speed. We also evaluate the efficiency of the commitment schemes and show that they are considerably fast.
With recent advances of quantum computation, new threats have closed in upon to the classical public key cryptosystems. In order to build more secure bit commitment schemes, this paper gave a survey of the new coming braid-based cryptography and then brought forward the first braid-based bit commitment protocol. The security proof manifests that the proposed protocol is computationally binding and information-theoretically hiding. Furthermore, the proposed protocol is also invulnerable to currently known quantum attacks.
The computational treatment of cryptography, and indeed any scientific treatment of a problem, is marked by its definitional side and by it constructive side. Results in this thesis better our understanding of both: on one side, they characterize the extent to which computational definitions capture the security of the basic task of symmetric encryption; on the other, they provide explicit bounds on the efficiency of commitment and secure two-party computation constructions. Specifically: (1) We relate the formal and computational treatments of symmetric encryption, obtaining a precise characterization of computational schemes whose computational semantics imply their formal semantics. We prove that this characterization is strictly weaker than previously-identified notions, and show how it may be realized in a simpler, more efficient manner. (2) We provide lower-bounds on the number of times a one-way permutation needs to be invoked (as a black-box) in order to construct statistically-binding commitments. Our bounds are tight for the case of perfectly-binding schemes. (3) We show that the secure computation of any two-party functionality can be performed in an optimal two rounds of communication even in a setting that accounts for concurrent execution with other protocols (i.e., the Universal Composability framework). Here, we rely on the assumption that parties have access to a common reference string; some sort of setup is known to be necessary.
Commitment schemes are cryptographic schemes that can be applied to zero-knowledge proof construction and blockchain construction. Recently, lattice-based cryptography has been intensively investigated due to the promising potential in quantum cryptography. Accordingly, commitment schemes based on lattice assumptions have been studied for practical applications. Notably, applications often require committing an arbitrary message with low communication costs, so commitment schemes must be satisfied with fewer length restrictions and fewer extensions to the messages. Several studies have been conducted to achieve the problem, including the study published by Baum et al. in 2018. However, the scheme in question still utilizes the message domain for extraneous purposes. We design a length-extension-free commitment scheme ComMWMin which the length of the message string is large relative to the length of the commitment string, improving on the commitment scheme of Baum et al. Furthermore, we prove that the hiding and binding properties of ComMWMare based on the hardness of the decisional search knapsack problem and extended search knapsack problems, respectively. Finally, we evaluate the computation costs of generating commitment value between ours and Baum et al.’s commitment scheme.
Abstract. Commitment schemes are among cryptography’s most im-portant building blocks. Besides their basic properties, hidingness and bindingness, for many applications it is important that the schemes ap-plied support proofs of knowledge. However, all existing solutions which have been proven to provide these protocols are only computationally hiding or are not resistant against quantum adversaries. This is not suitable for long-lived systems, such as long-term archives, where com-mitments have to provide security also in the long run. Thus, in this work we present a new post-quantum unconditionally hiding commit-ment scheme that supports (statistical) zero-knowledge protocols and allows to refreshes the binding property over time. The bindingness of our construction relies on the approximate shortest vector problem, a lattice problem which is conjectured to be hard for polynomial approxi-mation factors, even for a quantum adversary. Furthermore, we provide a protocol that allows the committer to prolong the bindingness prop-erty of a given commitment while showing in zero-knowledge fashion that the value committed to did not change. In addition, our construc-tion yields two more interesting features: one is the ability to “convert” a Pedersen commitment into a lattice-based one, and the other one is the construction of a hybrid approach whose bindingness relies on the discrete logarithm and approximate shortest vector problems.
Abstract. Key establishment protocols based on hardness assumptions, such as the discrete logarithm problem and the integer factorization problem, are vulnerable to quantum computer attacks, whereas the protocols based on other hardness assumptions, such as the conjugacy search problem and the decomposition search problem, can resist such attacks. The existing protocols based on the hardness assumptions which can resist quantum computer attacks are only passively secure. Compilers are used to convert a passively secure protocol to an actively secure protocol. Compilers involve some tools such as a signature scheme and a collision-resistant hash function. If there are only passively secure protocols but not a signature scheme based on the same assumption, then the application of existing compilers requires the use of such tools based on different assumptions. But the introduction of new tools, based on different assumptions, makes the new actively secure protocol rely on more than one hardness assumption. We offer an approach to derive an actively secure two-party protocol from a passively secure two-party protocol without introducing further hardness assumptions. This serves as a useful formal tool to transform any basic algebraic method of public key cryptography to the real world applicable cryptographic scheme.
The concept of zero-knowledge (ZK) has become of fundamental importance in cryptography. However, in a setting where entities are modeled by quantum computers, classical arguments for proving ZK fail to hold since, in the quantum setting, the concept of rewinding is not generally applicable. Moreover, known classical techniques that avoid rewinding have various shortcomings in the quantum setting. We propose new techniques for building quantum zero-knowledge (QZK) protocols, which remain secure even under (active) quantum attacks. We obtain computational QZK proofs and perfect QZK arguments for any NP language in the common reference string model. This is based on a general method converting an important class of classical honest-verifier ZK (HVZK) proofs into QZK proofs. This leads to quite practical protocols if the underlying HVZK proof is efficient. These are the first proof protocols enjoying these properties, in particular the first to achieve perfect QZK. As part of our construction, we propose a general framework for building unconditionally hiding (trapdoor) string commitment schemes, secure against quantum attacks, as well as concrete instantiations based on specific (believed to be) hard problems. This is of independent interest, as these are the first unconditionally hiding string commitment schemes withstanding quantum attacks. Finally, we give a partial answer to the question whether QZK is possible in the plain model. We propose a new notion of QZK, non-oblivious verifier QZK, which is strictly stronger than honest-verifier QZK but weaker than full QZK, and we show that this notion can be achieved by means of efficient (quantum) protocols.