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518 results · page 12 of 22
Joshua Brian Fitzgerald
Elliptic curve pairings are a powerful tool and a popular way to construct zero-knowledge proofs, which are beginning to be used in blockchains as a way to provide privacy in the transaction ledger.
Chitranjan Prasad Sah
The Robustness of any cryptographic technique gives us an idea about how that technique is asymptotically secure (asymptotic security), efficient, and can defeat different types of attacks on it. In this research, analysis and study have been done about how non-black-box technique called zero-knowledge proofs, can be used with RSA (Rivest, Shamir, Adleman) problem. One of the better algorithms for factoring needed by the RSA problem is general number field sieve factoring. The efficiency of general number field sieve factoring for RSA problem and discrete logarithm problem is analyzed and compared with each other; covariance between their asymptotic functions is calculated which clearly shows that they are strongly correlated with each other.
Shunrong Jiang, Jianqing Liu, Jingwei Chen, Yiliang Liu · 6 authors
Cloud outsourcing provides flexible storage and computation services for data users in a low cost, but it brings many security threats as the cloud server may not be fully trusted. Previous secure outsourcing solutions mostly assume that the server is honest-but-curious while the adversary model of a malicious server that may return incorrect results is rarely explored. Moreover, with the increasing popularity of verifiable computations, existing verification schemes are yet not efficient and cannot cater to different scenarios in practice. In this paper, we propose a blockchain-based verifiable search framework in the adversarial cloud outsourcing context. When outsourcing the encrypted data to the cloud or Interplanetary File System (IPFS), we also store the encrypted data index in a decentralized blockchain (i.e., Ethereum in this paper) which is public and cannot be modified. Once a user is authorized, he/she can flexibly obtain the query results and efficiently check the query integrity via the pre-deployed smart contract, without the need of the data owner being online. Moreover, for user's privacy protection, we construct a stealth authorization scheme to deliver the access authorization without any identity disclosure. Finally, theoretical analysis and performance evaluation validate the security and efficiency of our proposed framework.
Zarina Chokparova, Leon Urbas
No abstract is available for this record.
Robi Pedersen, Osmanbey Uzunkol
No abstract is available for this record.
George Teşeleanu
No abstract is available for this record.
Vadim Lyubashevsky, Ngoc Khanh Nguyen
No abstract is available for this record.
Sungwook Kim, Hyeonbum Lee, Jae Hong Seo
No abstract is available for this record.
Cyprien Delpech de Saint Guilhem, Emmanuela Orsini, Titouan Tanguy, Michiel Verbauwhede
No abstract is available for this record.
Mei Jiang, Dung Hoang Duong, Willy Susilo
No abstract is available for this record.
Xavier Arnal, Abraham Cano, Tamara Finogina, Javier Herranz
No abstract is available for this record.
Carsten Baum, Lennart Braun, Alexander Munch-Hansen, Peter Schöll
Zero-knowledge proof systems are usually designed to support computations for circuits over $$\mathbb {F}_2$$ or $$\mathbb {F}_p$$ for large p, but not for computations over $$\mathbb {Z}_{2^k}$$ , which all modern CPUs operate on. Although $$\mathbb {Z}_{2^k}$$ -arithmetic can be emulated using prime moduli, this comes with an unavoidable overhead. Recently, Baum et al. (CCS 2021) suggested a candidate construction for a designated-verifier zero-knowledge proof system that natively runs over $$\mathbb {Z}_{2^k}$$ . Unfortunately, their construction requires preprocessed random vector oblivious linear evaluation (VOLE) to be instantiated over $$\mathbb {Z}_{2^k}$$ . Currently, it is not known how to efficiently generate such random VOLE in large quantities. In this work, we present a maliciously secure, VOLE extension protocol that can turn a short seed-VOLE over $$\mathbb {Z}_{2^k}$$ into a much longer, pseudorandom VOLE over the same ring. Our construction borrows ideas from recent protocols over finite fields, which we non-trivially adapt to work over $$\mathbb {Z}_{2^k}$$ . Moreover, we show that the approach taken by the QuickSilver zero-knowledge proof system (Yang et al. CCS 2021) can be generalized to support computations over $$\mathbb {Z}_{2^k}$$ . This new VOLE-based proof system, which we call QuarkSilver, yields better efficiency than the previous zero-knowledge protocols suggested by Baum et al. Furthermore, we implement both our VOLE extension and our zero-knowledge proof system, and show that they can generate 13–50 million VOLEs per second for $${64}\,{\textrm{bit}}$$ to $${256}\,{\textrm{bit}}$$ rings, and evaluate $${1.3}\,\textrm{million}$$ $${64}\,{\textrm{bit}}$$ multiplications per second in zero-knowledge.
Rémi Clarisse
In our day to day life, information security is a predominant topic. More specifically, (online) users expect to be asked for consent and that service providers handle their personal data with care and integrity. This urges the design of systems enforcing such expectations. The field of cryptography provides such powerful privacy-preserving tools. In this thesis, we consider one of those tools: pairings over elliptic curves. We strongly diverge from the general approach, i.e. taking already standardized curves regardless of the cryptographic protocol, and suggest curves satisfying chosen criteria. The given curves in this thesis have more efficient operations in the first pairing group than the curves from the literature. We follow by giving a group signature scheme, a primitive enabling the anonymity of its users among the group they belong to, designed using pairing over elliptic curves. This group signature is efficient when compared to the state-of-the-art, thanks to the very nice interaction between two randomizable signature schemes, allowing us to get rid of costly zero-knowledge proofs.
Léo Robert, Daiki Miyahara, Pascal Lafourcade, Luc Libralesso · 5 authors
Suguru is a paper and pencil puzzle invented by Naoki Inaba. The goal of the game is to fill a grid with numbers between 1 and 5 while respecting three simple constraints. We first prove the NP-completeness of Suguru puzzle. For this we design gadgets to encode the PLANAR-CIRCUIT-SAT in a Suguru grid. We then design a physical Zero-Knowledge Proof (ZKP) protocol for Suguru. This ZKP protocol allows a prover to prove that he knows a solution of a Suguru grid to a verifier without leaking any information on the solution. To construct such a physical ZKP protocol, we only rely on a few physical cards and adapted encoding. For a Suguru grid with n cells, we only use 5n+5 cards. Moreover, we prove the three classical security properties of a ZKP: completeness, extractability, and zero-knowledge.
Marta Bellés-Muñoz, Barry Whitehat, Jordi Baylina, Vanesa Daza · 5 authors
Circuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from. The most efficient circuit-based zero-knowledge proofs use a pairing-friendly elliptic curve to generate and validate proofs. In particular, the circuits are built connecting wires that carry elements from a large prime field, whose order is determined by the number of elements of the pairing-friendly elliptic curve. In this context, it is important to generate an inner curve using this field, because it allows to create circuits that can verify public-key cryptography primitives, such as digital signatures and encryption schemes. To this purpose, in this article, we present a deterministic algorithm for generating twisted Edwards elliptic curves defined over a given prime field. We also provide an algorithm for checking the resilience of this type of curve against most common security attacks. Additionally, we use our algorithms to generate Baby Jubjub, a curve that can be used to implement elliptic-curve cryptography in circuits that can be validated in the Ethereum blockchain.
Kang Yang, Pratik Sarkar, Chenkai Weng, Xiao Wang
Zero-knowledge (ZK) proofs with an optimal memory footprint have attracted a lot of attention, because such protocols can easily prove very large computation with a small memory requirement. Such ZK protocol only needs O(M) memory for both parties, where M is the memory required to verify the statement in the clear. In this paper, we propose several new constant-round ZK protocols in this setting, which improve the concrete efficiency and, at the same time, enable sublinear amortized communication for circuits with some notion of relaxed uniformity. In the circuit-based model, where the computation is represented as a circuit over a field, our ZK protocol achieves a communication complexity of 1 field element per non-linear gate for any field size while keeping the computation very cheap. We implemented our protocol, which shows extremely high efficiency and affordability. Compared to the previous best-known implementation, we achieve 6x--7x improvement in computation and 3x--7x improvement in communication. When running on intro-level AWS instances, our protocol only needs one US dollar to prove one trillion AND gates (or 2.5 US dollars for one trillion multiplication gates over a 61-bit field). In the setting where part of the computation can be represented as a set of polynomials with a "degree-separated" format, we can achieve communication sublinear to the polynomial size: the communication only depends on the total number of distinct variables in all the polynomials and the highest degree of all polynomials, independent of the number of multiplications to compute all polynomials. Using the improved ZK protocol, we can prove matrix multiplication with communication proportional to the input size, rather than the number of multiplications. Proving the multiplication of two 1024 x 1024 matrices, our implementation, with one thread and 1 GB of memory, only needs 10 seconds and communicates 25 MB.
Carsten Baum, Lennart Braun, Alexander Munch-Hansen, Benoît Razet · 5 authors
Zero-knowledge proofs are highly flexible cryptographic protocols that are an important building block for many secure systems. Typically, these are defined with respect to statements that are formulated as arithmetic operations over a fixed finite field. This inflexibility is a disadvantage when it comes to complex programs, as some fields are more amenable to express certain operations than others. At the same time, there do not seem to be many proofs with a programming model similar to those found in modern computer architectures that perform arithmetic with 32 or 64 bit integers.
K N Devika, Ramesh Bhakthavatchalu
This paper concentrates on the hardware implementation of efficient and re- configurable elliptic curve digital signature algorithm (ECDSA) that is suitable for verifying transactions in Blockchain related applications. Despite ECDSA architecture being computationally expensive, the usage of a dedicated stand-alone circuit enables speedy execution of arithmetic operations. The prototype put forth supports N-bit elliptic curve cryptography (ECC) group operations, signature generation and verification over a prime field for any elliptic curve. The research proposes new hardware framework for modular multiplication and modular multiplicative inverse which is adopted for group operations involved in ECDSA. Every hardware design offered are simulated using modelsim register transfer logic (RTL) simulator. Field programmable gate array (FPGA) implementation of var- ious modules within ECDSA circuit is compared with equivalent existing techniques that is both hardware and software based to highlight the superiority of the suggested work. The results showcased prove that the designs implemented are both area and speed efficient with faster execution and less resource utilization while maintaining the same level of security. The suggested ECDSA structure could replace the software equivalent of digital signatures in hardware blockchain to thwart software attacks and to provide better data protection.
Jakob Jakob Povšič, Andrej Brodnik
Zero-Knowledge proofs (ZKPs) enable proving of mathematical statements, revealing nothing but their validity. We design an authentication sys-tem with a ZKP as a password verification mech-anism within the Extensible Authentication Pro-tocol (EAP) framework. Designing a secure pass-word authentication system requires us to adopt security practices for protecting ourselves against the vulnerabilities of passwords. Integrating said practices is not trivial because of the tight cou-pling with the password verification method.
Jung Hee Cheon, Dongwoo Kim, Duhyeong Kim, Keewoo Lee
The scaled inverse of a nonzero element $a(x)\in \mathbb{Z}[x]/f(x)$, where $f(x)$ is an irreducible polynomial over $\mathbb{Z}$, is the element $b(x)\in \mathbb{Z}[x]/f(x)$ such that $a(x)b(x)=c \pmod{f(x)}$ for the smallest possible positive integer scale $c$. In this paper, we investigate the scaled inverse of $(x^i-x^j)$ modulo cyclotomic polynomial of the form $\Phi_{p^s}(x)$ or $\Phi_{p^s q^t}(x)$, where $p, q$ are primes with $p<q$ and $s, t$ are positive integers. Our main results are that the coefficient size of the scaled inverse of $(x^i-x^j)$ is bounded by $p-1$ with the scale $p$ modulo $\Phi_{p^s}(x)$, and is bounded by $q-1$ with the scale not greater than $q$ modulo $\Phi_{p^s q^t}(x)$. Previously, the analogous result on cyclotomic polynomials of the form $\Phi_{2^n}(x)$ gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of $\{x^k\}_{k\in\mathbb{Z}}$ in $\mathbb{Z}[x]/\Phi_{pq}(x)$ which might be of independent interest.
Ye Zhang, Shuo Wang, Xian Zhang, Jiangbin Dong · 10 authors
Zero-knowledge proof (ZKP) is a promising cryptographic protocol for both computation integrity and privacy. It can be used in many privacy-preserving applications including verifiable cloud outsourcing and blockchains. The major obstacle of using ZKP in practice is its time-consuming step for proof generation, which consists of large-size polynomial computations and multi-scalar multiplications on elliptic curves. To efficiently and practically support ZKP in real-world applications, we propose PipeZK, a pipelined accelerator with two subsystems to handle the aforementioned two intensive compute tasks, respectively. The first subsystem uses a novel dataflow to decompose large kernels into smaller ones that execute on bandwidth-efficient hardware modules, with optimized off-chip memory accesses and on-chip compute resources. The second subsystem adopts a lightweight dynamic work dispatch mechanism to share the heavy processing units, with minimized resource underutilization and load imbalance. When evaluated in 28 nm, PipeZK can achieve 10x speedup on standard cryptographic benchmarks, and 5x on a widely-used cryptocurrency application, Zcash.
Javier Silva Velón
No abstract is available for this record.
Hongxun Huang, Ziyuan Liu, Raylin Tso
Blind signatures allow a user to obtain a signature without revealing message information to the signer. However, in many cases, the signer must record additional information relevant to the signature. Therefore, the concept of partially blind signature is introduced that enables the signer to obtain some information from the signed message. With the development of blockchain technology, users increasingly use Bitcoin for purchases and transactions with coin providers. Some studies have indicated that Elliptic Curve Digital Signature Algorithm (ECDSA)-based blind signatures are compatible with Bitcoin because they prevent the linking of sensitive information due to the untamability of Bitcoin. However, these approaches are not sufficiently flexible because blind signatures do not allow the signer to obtain any information. Here, we propose an ECDSA-based partially blind signature scheme. Security proofs are provided to demonstrate that the proposed scheme have satisfactory unforgeability and blindness. To the best of our knowledge, compared with other state-of-the-art schemes, our scheme is the first ECDSA-based partially blind signature scheme compatible with the current Bitcoin protocol.
Handong Cui, Tsz Hon Yuen
No abstract is available for this record.