Blockchain Papers

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Oct 17, 2024
1 cites
CredVault: A Credential Management System based on Zero-Knowledge Proofs

Harsh Gupta, Khushi S. Kasat, Abhijeet R. Raipurkar, Praful R. Pardhi

As digital identities become increasingly valuable and vulnerable, the protection of personal credentials has become a critical concern. This paper introduces a fresh perspective on credential management, focusing on enhancing privacy and security. We propose a user-centric approach that revolves around the idea of creating a safe space for digital credentials within decentralized wallets. By leveraging existing social login mechanisms and establishing secure tokenized containers for credentials, users can securely store and manage their digital identity. Our framework aims to empower individuals by providing them with control over their credentials while minimizing the risk of exposure to third parties. This paper outlines the core concepts and objectives of our approach, highlighting its potential to revolutionize the way we manage and protect our digital identities.

Access Control and Trust
Cryptography and Data Security
Cloud Data Security Solutions
Original source
Oct 17, 2024
2 cites
BDIMS: A Blockchain Based Digital Identity Management System with Zero Knowledge Proof

Md. Humayan Kabir Rupok, K. M. Azharul Hasan

The world is rapidly heading towards digitization and digital documentation.The COVID-19 pandemic has highlighted the significance of digitization in our daily lives.Nowadays, fake documents are widely available and easy to obtain, harming both our financial system and social trust.Consequently, there is a growing demand for procedures to verify and authenticate various crucial documents, including transactional, financial, governmental, and personal certificates, as well as educational certificates.This type of practice can be done using blockchain and cryptography technology.In this paper, we propose a Blockchain based Digital Identity Management System (BDIMS) that empowers organizations to generate instantaneously authenticated and tamper-resistant digital credentials.It issues a signed document and stores the signature on the blockchain.The verifier can easily verify the signature from the blockchain instantly using the digital signature concept.BDIMS also provides a QR-code system for real-time identity verification.It also introduces zero-knowledge proof for verifying the part of an identity without revealing the original statement.Furthermore, a user can store and share all their identities on a single platform using BDIMS.The proposed model effectively addresses the shortcomings of traditional methods by ensuring a comprehensive and streamlined approach.It successfully bridges the gaps and overcomes the difficulties inherent in conventional document verification systems, meeting all the necessary criteria for a robust and reliable verification process.

Open access
Blockchain Technology Applications and Security
Cryptography and Data Security
Cloud Data Security Solutions
Original source
Oct 17, 2024
3 cites
Age Verification using Zero-knowledge Proof

Chaitali Patil, Sanjita Jain, Rupprashik A. Khare, Samyak Lahire

This research paper explores the zero-knowledge proofs (ZKPs) and integration of blockchain technology to develop a secure age verification system, specifically aimed at verifying the age of a person who is driving a vehicle (driver) as at least 18 years in the context of traffic management. Traditional authentication methods like passwords and biometrics have significant vulnerabilities, such as being susceptible to brute-force attacks, phishing, and data breaches. Unlike traditional systems and self-sovereign identity (SSI) solutions, ZKPs ensure the most secure method for authentication and verification without revealing sensitive information. The proposed implemented system utilizes blockchain-based verifiable credentials, decentralized identity, ZKPs and Polygon ID Wallet for verifying driver credentials securely. By leveraging decentralized ledgers, cryptographic protocols and zero-knowledge our system maintains transparency and immutability of records while safeguarding individual privacy and security. This paper also focuses future directions of the proposed system underscoring its potential to transform user verification processes across different sectors with high privacy requirements.

Generative Adversarial Networks and Image Synthesis
Face recognition and analysis
Advanced Neural Network Applications
Original source
Oct 16, 2024·arXiv
5 cites
fAmulet: Finding Finalization Failure Bugs in Polygon zkRollup

Zihao Li, Xinghao Peng, Zheyuan He, Xiapu Luo · 5 authors

Zero-knowledge layer 2 protocols emerge as a compelling approach to overcoming blockchain scalability issues by processing transactions through the transaction finalization process. During this process, transactions are efficiently processed off the main chain. Besides, both the transaction data and the zero-knowledge proofs of transaction executions are reserved on the main chain, ensuring the availability of transaction data as well as the correctness and verifiability of transaction executions. Hence, any bugs that cause the transaction finalization failure are crucial, as they impair the usability of these protocols and the scalability of blockchains. In this work, we conduct the first systematic study on finalization failure bugs in zero-knowledge layer 2 protocols, and define two kinds of such bugs. Besides, we design fAmulet, the first tool to detect finalization failure bugs in Polygon zkRollup, a prominent zero-knowledge layer 2 protocol, by leveraging fuzzing testing. To trigger finalization failure bugs effectively, we introduce a finalization behavior model to guide our transaction fuzzer to generate and mutate transactions for inducing diverse behaviors across each component (e.g., Sequencer) in the finalization process. Moreover, we define bug oracles according to the distinct bug definitions to accurately detect bugs. Through our evaluation, fAmulet can uncover twelve zero-day finalization failure bugs in Polygon zkRollup, and cover at least 20.8% more branches than baselines. Furthermore, through our preliminary study, fAmulet uncovers a zero-day finalization failure bug in Scroll zkRollup, highlighting the generality of fAmulet to be applied to other zero-knowledge layer 2 protocols. At the time of writing, all our uncovered bugs have been confirmed and fixed by Polygon zkRollup and Scroll zkRollup teams.

Open access
2 source records
cs.CR
Blockchain Technology Applications and Security
IoT and Edge/Fog Computing
Original source
Oct 16, 2024·Research Square
1 cites
Secure Mobile Authentication With Blockchain

Naim Ajlouni, Vedat Coşkun, Büşra Özdenizci

No abstract is available for this record.

Open access
User Authentication and Security Systems
Blockchain Technology Applications and Security
Advanced Malware Detection Techniques
Original source
Oct 15, 2024·Canadian Journal of Physics
2 cites
Quantum computational complexity and symmetry

Soorya Rethinasamy, Margarite L. LaBorde, Mark M. Wilde

Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the difficulty of symmetry-testing problems involving a unitary representation of a group and a state or a channel that is being tested. In particular, we prove that various such symmetry-testing problems are complete for bounded-error quantum polynomial time, quantum Merlin–Arthur (QMA), quantum statistical zero-knowledge, two-message quantum interactive proofs (QIPs), two-message QIPs restricted to entanglement-breaking provers, and QIPs, thus spanning the prominent classes of the QIP hierarchy and forging a nontrivial connection between symmetry and quantum computational complexity. Finally, we prove the inclusion of two Hamiltonian symmetry-testing problems in QMA and quantum Arthur–Merlin, while leaving it as an intriguing open question to determine whether these problems are complete for these classes.

Open access
History and advancements in chemistry
Original source
Oct 15, 2024
2 cites
Privacy-preserving Attribute Based Credentials for 6G networks

Andreas Künz, Rodrigo Asensio-Garriga, Jesús García-Rodríguez, Jorge Bernal Bernabé · 7 authors

This paper provides an overview of the integration of privacy preserving Attribute Based Credentials (p-ABC) into the 3GPP 5G Advanced system as well as into the European Project RIGOUROUS (secuRe desIGn and deplOyment of trUsthwoRthy cOntinUum computing 6G Services) for 6G. The differences in the access and device (or user) authentication and authorization in the 3GPP system and the concepts of p-ABC require architectural changes in the main procedures. The novel architecture and procedures of p-ABC support in 5G Advanced are described along with an overview of the 6G RIGOUROUS architecture highlighting the updated zero-touch onboarding of devices into the system. This integration enhances the 5G+ system to support privacy goals such as minimal disclosure or controlled linkability through zero-knowledge proofs.

Privacy-Preserving Technologies in Data
Cryptography and Data Security
Blockchain Technology Applications and Security
Original source
Oct 15, 2024
0 cites
Quantum Zero-Knowledge Proof

Tao Shang

No abstract is available for this record.

Cryptography and Data Security
Quantum Computing Algorithms and Architecture
Benford’s Law and Fraud Detection
Original source
Oct 12, 2024·Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
1 cites
Batch Lattice-Based Designated-Verifier ZK-SNARKs for R1CS

Xi Lin, Han Xia, Yongqiang Li, Mingsheng Wang

No abstract is available for this record.

Cryptography and Data Security
Cryptographic Implementations and Security
Security in Wireless Sensor Networks
Original source
Oct 12, 2024·Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
5 cites
Efficient Zero Knowledge for Regular Language

Michael W. Raymond, Gillian Evers, Jan Ponti, Diya Krishnan · 5 authors

No abstract is available for this record.

Algorithms and Data Compression
semigroups and automata theory
Cryptography and Data Security
Original source
Oct 11, 2024·arXiv (Cornell University)
0 cites
SoK: Verifiable Cross-Silo FL

Aleksei Korneev, Jan Ramon

Federated Learning (FL) is a widespread approach that allows training machine learning (ML) models with data distributed across multiple devices. In cross-silo FL, which often appears in domains like healthcare or finance, the number of participants is moderate, and each party typically represents a well-known organization. For instance, in medicine data owners are often hospitals or data hubs which are well-established entities. However, malicious parties may still attempt to disturb the training procedure in order to obtain certain benefits, for example, a biased result or a reduction in computational load. While one can easily detect a malicious agent when data used for training is public, the problem becomes much more acute when it is necessary to maintain the privacy of the training dataset. To address this issue, there is recently growing interest in developing verifiable protocols, where one can check that parties do not deviate from the training procedure and perform computations correctly. In this paper, we present a systematization of knowledge on verifiable cross-silo FL. We analyze various protocols, fit them in a taxonomy, and compare their efficiency and threat models. We also analyze Zero-Knowledge Proof (ZKP) schemes and discuss how their overall cost in a FL context can be minimized. Lastly, we identify research gaps and discuss potential directions for future scientific work.

Open access
2 source records
cs.LG
cs.AI
cs.CR
Original source
Oct 11, 2024·International Journal of Computer Science and Engineering Research and Development
0 cites
ZERO-KNOWLEDGE PROOFS FOR PRIVACY-PRESERVING AI AUTHENTICATION

Narayana Gaddam

As machine learning spreads into fields of use that demand secure and private authentication, ensuring such authentication is becoming increasingly critical.Zero Knowledge Proofs (ZKPs) have been presented as a cryptographic technique of transforming authentication without data leakage [1].In this research, the use of ZKPs in the AI authentication frameworks is looking into privacy, security and scalability.The model predictions are verified by the proposed system using advanced ZKP protocols like zkSNARKs and zkSTARKs without revealing model parameters or user inputs [3].Our system is able to reach better computational efficiency and lower computation overhead through incorporation of Mystique conversion protocols [7] and fast ZK inference protocols such as ezDPS [6].Results of experiments [5] show that frameworks with ZKP integrated authentication perform better than the standard encryption with respect to both security and performance in decentralized machine learning regimes.Moreover, the solution facilitates verifiability in Federated Learning by integrating blockchain, which helps to increase transparency and trust [4].To overcome the data leakage issue, ZKPs are explored for use in decentralized AI frameworks where secure model deployment is required to generate personalized advice [4].As this research shows, ZKPs offer transformative properties which can be used for authentication in AI systemssuch as in healthcare, finance or IoT network and thus increase the trust in AI driven solutions.

Open access
Cryptography and Data Security
Privacy-Preserving Technologies in Data
Original source
Oct 11, 2024·Journal of Sensor and Actuator Networks
1 cites
Efficient Zero-Knowledge Proofs for Set Membership in Blockchain-Based Sensor Networks: A Novel OR-Aggregation Approach

Alexandr Kuznetsov, Emanuele Frontoni, Marco Arnesano, Kateryna Kuznetsova

Blockchain-based sensor networks offer promising solutions for secure and transparent data management in IoT ecosystems. However, efficient set membership proofs remain a critical challenge, particularly in resource-constrained environments. This paper introduces a novel OR-aggregation approach (where “OR” refers to proving that an element equals at least one member of a set without revealing which one) for zero-knowledge set membership proofs, tailored specifically for blockchain-based sensor networks. We provide a comprehensive theoretical foundation, detailed protocol specification, and rigorous security analysis. Our implementation incorporates optimization techniques for resource-constrained devices and strategies for integration with prominent blockchain platforms. Extensive experimental evaluation demonstrates the superiority of our approach over existing methods, particularly for large-scale deployments. Results show significant improvements in proof size, generation time, and verification efficiency. The proposed OR-aggregation technique offers a scalable and privacy-preserving solution for set membership verification in blockchain-based IoT applications, addressing key limitations of current approaches. Our work contributes to the advancement of efficient and secure data management in large-scale sensor networks, paving the way for wider adoption of blockchain technology in IoT ecosystems.

Open access
3 source records
Blockchain Technology Applications and Security
IoT and Edge/Fog Computing
Security in Wireless Sensor Networks
Original source
Oct 11, 2024·IEEE Transactions on Circuits and Systems I Regular Papers
9 cites
ReZK: A Highly Reconfigurable Accelerator for Zero-Knowledge Proof

Hao Zhou, Changxu Liu, Lan Yang, Li Shang · 5 authors

Zero-knowledge proof (ZKP) plays a significant role in privacy protection technology. However, the proof generation phase requires considerable time and hardware resources. In this phase, Number Theoretic Transform or Inverse Number Theoretic Transform (NTT/INTT) in polynomial computation, as well as Multiple Scalar Multiplication (MSM), are bottlenecks that dominate the execution time. In this paper, we propose a highly reconfigurable accelerator ReZK to accelerate ZKP proof generation phase, focusing on NTT/INTT and MSM. According to the configurations, ReZK can be configured as NTT, INTT, and MSM with variable sizes and bit-widths by adjusting the data path between on-chip memories and arithmetic cores. As the basic unit of arithmetic cores, the reconfigurable processing element (PE) in ReZK is composed of pipelined modular multipliers and modular adders that support variable bit-widths. It can perform butterfly or arithmetic operations. Based on the reconfigurable PEs, the ReZK core can implement NTT/INTT with different sizes and bit-widths, or a fully pipelined point adder (PADD). Additionally, we propose a modularized MSM scheduling architecture to support various bit-widths. The on-chip memories are also well organized for reuse. In NTT/INTT mode, 4-way 256-bit or 2-way 384-bit NTT/INTT can be computed in parallel. In MSM mode, for different elliptic curves, ReZK is capable of processing 4-way 256-bit or 2-way 384-bit MSM in parallel.

Security and Verification in Computing
Radiation Effects in Electronics
Numerical Methods and Algorithms
Original source
Oct 9, 2024·arXiv (Cornell University)
0 cites
Checker Bug Detection and Repair in Deep Learning Libraries

Nima Shiri Harzevili, Mohammad Mahdi Mohajer, Jiho Shin, Moshi Wei · 11 authors

Checker bugs in Deep Learning (DL) libraries are critical yet not well-explored. These bugs are often concealed in the input validation and error-checking code of DL libraries and can lead to silent failures, incorrect results, or unexpected program behavior in DL applications. Despite their potential to significantly impact the reliability and performance of DL-enabled systems built with these libraries, checker bugs have received limited attention. We present the first comprehensive study of DL checker bugs in two widely-used DL libraries, i.e., TensorFlow and PyTorch. Initially, we automatically collected a dataset of 2,418 commits from TensorFlow and PyTorch repositories on GitHub from Sept. 2016 to Dec. 2023 using specific keywords related to checker bugs. Through manual inspection, we identified 527 DL checker bugs. Subsequently, we analyzed these bugs from three perspectives, i.e., root causes, symptoms, and fixing patterns. Using the knowledge gained via root cause analysis of checker bugs, we further propose TensorGuard, a proof-of-concept RAG-based LLM-based tool to detect and fix checker bugs in DL libraries via prompt engineering a series of ChatGPT prompts. We evaluated TensorGuard's performance on a test dataset that includes 92 buggy and 135 clean checker-related changes in TensorFlow and PyTorch from January 2024 to July 2024. Our results demonstrate that TensorGuard has high average recall (94.51\%) using Chain of Thought prompting, a balanced performance between precision and recall using Zero-Shot prompting and Few-Shot prompting strategies. In terms of patch generation, TensorGuard achieves an accuracy of 11.1\%, which outperforms the state-of-the-art bug repair baseline by 2\%. We have also applied TensorGuard on the latest six months' checker-related changes (493 changes) of the JAX library from Google, which resulted in the detection of 64 new checker bugs.

Open access
Machine Learning and Data Classification
Advanced Neural Network Applications
Advanced Data Storage Technologies
Original source
Oct 9, 2024
2 cites
Building Trustworthy AI Systems: AI Inference Verification with Blockchain and Zero-Knowledge Proofs

Patrizio Germani, Michelangelo Amoruso Manzari, Riccardo Magni, Paolo Dibitonto · 6 authors

In recent years, the use of deep learning models in sensitive applications increased exponentially. There is a strong need of having a mechanisms for a transparent and secure inference verification. To this end, we propose a system leveraging Zero-Knowledge Proofs (ZKPs) and Blockchain technologies to ensure the validity of model inferences without revealing neither input data nor model details.In this paper, we propose a system that is capable of making non-interactive proofs that are verified on a Blockchain thus creating a trustless environment between the prover and the verifier. The solution is based on the Easy Zero-Knowledge Inference (EZKL) [1] library and leverages ZK-SNARK [2] proofs. We provide a detailed descriptions of the system’s architecture, the implementation as well as the benefits of this approach in enhancing transparency and security in Artificial Intelligence (AI) applications.

Adversarial Robustness in Machine Learning
Explainable Artificial Intelligence (XAI)
Ethics and Social Impacts of AI
Original source
Oct 8, 2024
0 cites
Enhanced DeFi Security on XRPL with Zero-Knowledge Proofs and Speaker Verification

Pavel Pantiukhov, Dmitrii Koriakov, Tatiana V. Petrova, Jeovane Honório Alves · 6 authors

Blockchain technology has consistently attracted attention for its transparency, decentralization, and security. More everyday users, without technical expertise, are now using blockchain and cryptocurrencies to store funds. As decentralized finance (DeFi) rises, security and privacy challenges have emerged, particularly the risk of losing funds due to leaked private keys. Consequently, enhancing security with user-friendly authentication methods is crucial. Voice authentication is a promising solution to add a security layer to the blockchain, but it is difficult to implement in DeFi without compromising decentralization and data confidentiality. Furthermore, advances in deep learning in voice cloning pose risks to voice-based systems. To address these issues, we propose the ZK Verify Voice Authentication System, which enables spoofing-aware speaker verification for the XRP Ledger (XRPL). Confidentiality is ensured by integrating voice embeddings with zero-knowledge proofs (zk-SNARKs). Voice embeddings serve as digital signatures, with only their hash stored on XRPL. Our system improves security and user experience by allowing individuals to prove their identity without exposing voice data. This approach provides robust security and privacy for DeFi participants, while remaining accessible to those without technical expertise.

Natural Language Processing Techniques
Speech Recognition and Synthesis
Original source
Oct 8, 2024·IEEE Transactions on Vehicular Technology
20 cites
Anonymous Authentication and Information Sharing Scheme Based on Blockchain and Zero Knowledge Proof for VANETs

Xiaohong Zhang, Xingxing Chen, Shuling Liu, Shaojiang Zhong

In recent years, with the increasing integration of intelligent modules into vehicles, intelligent transportation systems (ITS) have increasingly assumed a pivotal role in augmenting driver safety. As an ITS, vehicle ad hoc networks (VANETs) not only establish a secure traffic environment for users but also provides them with an efficient means of exchanging traffic information. However, during vehicle communication processes, security challenges such as the leakage of vehicle privacy information and tampering with shared task information must be addressed. Therefore, this paper proposes a decentralized anonymous authentication and secure traffic task information-sharing scheme based on blockchain and zk-SNARK. Specifically, the proposed scheme utilizes blockchain technology and the interplanetary file system (IPFS) to securely and efficiently store and share task information in a fully decentralized manner. Vehicle users anonymously participate in tasks within VANETs using pseudonym information generated during registration with a trusted authority (TA). Additionally, by employing zk-SNARK to generate zero-knowledge proofs, the validity and integrity of task information can be verified without revealing any private information. Performance comparisons indicate that the proposed scheme enhances the security of vehicle-to-roadside unit (V2R) and vehicle-to-vehicle (V2V) communications while reducing communication and computational costs.

Vehicular Ad Hoc Networks (VANETs)
Privacy-Preserving Technologies in Data
Cloud Data Security Solutions
Original source
Oct 7, 2024·IACR Communications in Cryptology
2 cites
Constant-Round YOSO MPC Without Setup

Sebastian Kolby, Divya Ravi, Sophia Yakoubov

YOSO MPC (Gentry et al., Crypto 2021) is a new MPC framework where each participant can speak at most once. This models an adaptive adversary’s ability to watch the network and corrupt or destroy parties it deems significant based on their communication. By using private channels to anonymous receivers (e.g. by encrypting to a public key whose owner is unknown), the communication complexity of YOSO MPC can scale sublinearly with the total number N of available parties, even when the adversary’s corruption threshold is linear in N (e.g. just under N/2). It was previously an open problem whether YOSO MPC can achieve guaranteed output delivery in a constant number of rounds without relying on trusted setup. In this work, we show that this can indeed be accomplished. We demonstrate three different approaches: the first two (which we call YaOSO and YOSO-GLS) use two and three rounds of communication, respectively. Our third approach (which we call YOSO-LHSS) uses O(d) rounds, where d is the multiplicative depth of the circuit being evaluated; however, it can be used to bootstrap any constant-round YOSO protocol that requires setup, by generating that setup within YOSO-LHSS. Though YOSO-LHSS requires more rounds than our first two approaches, it may be more practical, since the zero knowledge proofs it employs are more efficient to instantiate. As a contribution of independent interest, we introduce a verifiable state propagation UC functionality, which allows parties to send private message which are verifiably derived in the “correct” way (according to the protocol in question) to anonymous receivers. This is a natural functionality to build YOSO protocols on top of.

Open access
Cryptography and Data Security
Complexity and Algorithms in Graphs
Privacy-Preserving Technologies in Data
Original source
Oct 7, 2024·IACR Communications in Cryptology
3 cites
Efficient Maliciously Secure Oblivious Exponentiations

Carsten Baum, Jens Berlips, W Q Chen, Ivan Damgård · 20 authors

Oblivious Pseudorandom Functions (OPRFs) allow a client to evaluate a pseudorandom function (PRF) on her secret input based on a key that is held by a server. In the process, the client only learns the PRF output but not the key, while the server neither learns the input nor the output of the client. The arguably most popular OPRF is due to Naor, Pinkas and Reingold (Eurocrypt 2009). It is based on an Oblivious Exponentiation by the server, with passive security under the Decisional Diffie-Hellman assumption. In this work, we strengthen the security guarantees of the NPR OPRF by protecting it against active attacks of the server. We have implemented our solution and report on the performance. Our main result is a new batch OPRF protocol which is secure against maliciously corrupted servers, but is essentially as efficient as the semi-honest solution. More precisely, the computation (and communication) overhead is a multiplicative factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>o</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> as the batch size increases. The obvious solution using zero-knowledge proofs would have a constant factor overhead at best, which can be too expensive for certain deployments. Our protocol relies on a novel version of the DDH problem, which we call the Oblivious Exponentiation Problem (OEP), and we give evidence for its hardness in the Generic Group model. We also present a variant of our maliciously secure protocol that does not rely on the OEP but nevertheless only has overhead <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>o</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> over the known semi-honest protocol. Moreover, we show that our techniques can also be used to efficiently protect threshold blind BLS signing and threshold ElGamal decryption against malicious attackers.

Open access
Cryptography and Data Security
Privacy-Preserving Technologies in Data
Advanced Steganography and Watermarking Techniques
Original source
Oct 7, 2024·Panamerican mathematical journal.
18 cites
Mathematical Approaches to Cryptographic System Design

Manoj Tarambale

In the digital age, cryptographic systems are the most important part of safe communication. To protect data security, confidentiality, and validity, they need strong design frameworks. The math methods used in this paper are very important for designing and analyzing secure systems. As basic ideas, it looks at number theory, math, and complexity theory, with an emphasis on both old and new methods. Some important topics are the creation of prime numbers, modular arithmetic, elliptic curves, and finite fields, which are the basis for many encryption methods. The paper also talks about how complexity theory can be used to measure the strength of cryptography. It specifically talks about issues with discrete logarithms and integer factorization, which are at the heart of popular protocols like RSA and ECC. It also looks into lattice-based cryptography, which is seen as a strong option to quantum threats, and shows how hard it is to solve lattice issues. The study also looks at the design principles of symmetric cryptography, mainly block ciphers and stream ciphers, and how they use permutation groups and linear algebra to make sure that key plans and spread methods are safe. The paper also looks at secure hash functions, focusing on collision resistance, pre-image resistance, and how they are made using mathematics concepts such as Merkle-Damgård and sponge functions. Advanced topics like homomorphic encryption and zero-knowledge proofs show how mathematics and cryptography are increasingly coming together. They show how they can be used to make operations safe on protected data and privacy-preserving protocols. This paper gives a full picture of how mathematical theories and methods are used to build strong cryptographic systems by combining strict mathematical models with real-world cryptographic needs. The discussion stresses that the field is always changing because of new threats and improvements in computers. It also calls for constant scientific progress to make cryptography stronger against future problems.

Chaos-based Image/Signal Encryption
Computability, Logic, AI Algorithms
Original source
Oct 7, 2024·IACR Communications in Cryptology
5 cites
The Uber-Knowledge Assumption: A Bridge to the AGM

Balthazar Bauer, Pooya Farshim, Patrick Harasser, Markulf Kohlweiss

The generic-group model (GGM) and the algebraic-group model (AGM) have been exceptionally successful in proving the security of many classical and modern cryptosystems. These models, however, come with standard-model uninstantiability results, raising the question of whether the schemes analyzed under them can be based on firmer standard-model footing. We formulate the uber-knowledge (UK) assumption, a standard-model assumption that naturally extends the uber-assumption family to knowledge-type problems. We justify the soundness of UK in both the bilinear GGM and the bilinear AGM. Along the way we extend these models to account for hashing into groups, an adversarial capability that is available in many concrete groups—In contrast to standard assumptions, hashing may affect the validity of knowledge assumptions. These results, in turn, enable a modular approach to security in the GGM and the AGM. As example applications, we use the UK assumption to prove knowledge soundness of Groth's zero-knowledge SNARK (EUROCRYPT 2016) and of KZG polynomial commitments (ASIACRYPT 2010) in the standard model, where for the former we reuse the existing proof in the AGM without hashing.

Open access
Cryptography and Data Security
Blockchain Technology Applications and Security
Privacy-Preserving Technologies in Data
Original source