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Add a method, remove a method, edit datasets, demystifying the rsa algorithm: an intuitive introduction for novices in cybersecurity.

5 Aug 2023  ·  Zhengping Jay Luo , Ruowen Liu , Aarav Mehta , Md Liakat Ali · Edit social preview

Given the escalating importance of cybersecurity, it becomes increasingly beneficial for a diverse community to comprehend fundamental security mechanisms. Among these, the RSA algorithm stands out as a crucial component in public-key cryptosystems. However, understanding the RSA algorithm typically entails familiarity with number theory, modular arithmetic, and related concepts, which can often exceed the knowledge base of beginners entering the field of cybersecurity. In this study, we present an intuitively crafted, student-oriented introduction to the RSA algorithm. We assume that our readers possess only a basic background in mathematics and cybersecurity. Commencing with the three essential goals of public-key cryptosystems, we provide a step-by-step elucidation of how the RSA algorithm accomplishes these objectives. Additionally, we employ a toy example to further enhance practical understanding. Our assessment of student learning outcomes, conducted across two sections of the same course, reveals a discernible improvement in grades for the students.

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• Corpus ID: 16068349

The RSA Algorithm

• Evgeny Milanov , In , +2 authors Leonard
• Published 2009
• Computer Science, Mathematics

124 Citations

Distinguish from symmetric and asymmetric crypto systems. cite the strengths and shortcomings of the each system, asymmetric cryptosystems, nhskca: a new heuristic for symmetric key cryptographic algorithm, secret sharing and authentication using visual cryptography with rsa algorithm, data encryption and decryption using rsa algorithm in a network environment, fast implementation of the rivest-shamir-adleman (rsa) algorithm with robust packet data loss detection function, securing distributed database using elongated rsa algorithm, post quantum cryptography: comparison between rsa and mceliece, a public key cryptography based on the m-injectivity of $z_{pq}$ over itself, secure mailing system, 2 references, related papers.

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Information Technology Journal

• Vol 12 (9), 2013

Research Article

Analysis and research of the rsa algorithm.

Received: March 27, 2013;   Accepted: May 07, 2013;   Published: July 03, 2013

How to cite this article

Introduction.

ACKNOWLEDGMENTS

• Kahata, A., 2005. Cryptography and Network Security. Tsinghua University Press, Beijing, China.
• Chen, Z., 2012. The encryption algorithm and security of RSA. J. Hengyang Normal Univ., 12: 69-69.
• Wei, X., Z. Li and Y. Zhu, 2011. On the RSA algorithm and application. J. Honghe Univ., 4: 31-32.
• Shi, Z., 2007. Computer Network Security Tutorial. Tsinghua University Press, Beijing, China.
• Cai, C. and Y. Lu, 2011. Asymmetric encryption JAVA and VC. Comput. Knowled. Technol., 18: 4306-4307.
• He, C. and H. Wu, 2004. Public key RSA algorithm is applied to several problems. Mod. Comput., 178: 72-74.
• Buchmann, J., 2001. Einfuhrung in die Kryptographie [Introduction to Cryptography]. 2nd Edn., Springer, Berlin, Germany.
• Wang, H. and R. Song, 2011. The length of the key influences the degree of security of the RSA system. Comput. Knowledge Technol., 10: 7104-7105.
• Chen, C. and Z. Zhu, 2006. Application of RSA algorithm and implementation details. Comput. Eng. Sci., 9: 13-14.
• Shi, Z., Q. Tan and H. Duan, 2008. The research and application of the RSA algorithm in the digital signature. Microcomput. Appl., 6: 50-51.
• Zhang, Y. and T. Cao, 2011. Application of encryption based on RSA algorithm. Sci. Technol. Advisory (Technol. Admin.), 25: 79-80.
• Zhang, S., W. Wan and J. Zhang, 2009. Applied Cryptography. Xi'an Electronic and Science University Press, Xi'an, China.
• Si, H. and B. Tang, 2009. Application of RSA and its application in an encrypted file. Comput. Telecommun., 6: 76-77.
• Guo, H., 2011. Efficient implementation of RSA algorithm based on C language. Mod. Comput., 8: 14-14.
• Internet Data Center, 2011. Data encryption technology of [DB/OL]. http://zy.zhku.edu.cn/info/kcln/10/3.htm.

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https://www.nist.gov/blogs/cybersecurity-insights/implementation-challenges-privacy-preserving-federated-learning

Cybersecurity Insights

a NIST blog

Implementation Challenges in Privacy-Preserving Federated Learning

In this post, we talk with Dr. Xiaowei Huang and Dr. Yi Dong (University of Liverpool), Dr. Mat Weldon ( United K ingdom (UK) Office of National Statistics (ONS)), and Dr. Michael Fenton (Trūata) who were winners in the UK-US Privacy-Enhancing Technologies ( PETs) Prize Challenges. We discuss implementation challenges of privacy-preserving federated learning (PPFL) - specifically, the areas of threat modeling and real world deployments.

Threat Modeling

In research on privacy-preserving federated learning (PPFL), the protections of a PPFL system are usually encoded in a threat model  that defines what kinds of attackers the system can defend against. Some systems assume that attackers will eavesdrop on the system’s operation but won’t be able to affect its operation (a so-called honest but curious attacker), while others assume that attackers may modify or break the system’s operation (an active or fully malicious attacker). Weaker attackers are generally easier to defend against than stronger ones.

Unfortunately, it remains challenging to determine whether a threat model is realistic. In the real world, will attackers be honest but curious, or fully malicious? Or somewhere in between? It’s often very difficult to say with confidence—and making the wrong choice may result in deployment of a system that is not sufficiently well-defended. Moreover, it can be difficult even to compare different threat models to determine their relative strength.

Authors: What assumptions do system designers make about the capabilities of attackers when designing a threat model?

Dr. Xiaowei Huang and Dr. Yi Dong, University of Liverpool:  Depending on the assumptions, different threat models enable the attacker with different capabilities. For example, an attacker can eavesdrop on communications between agents and use the observations to figure out the secrets (e.g., reconstruct the global model). Another attacker may tamper with the labels of a local dataset to induce erroneous predictions. A local agent can also be an attacker, in the sense that they can inject backdoors into the global model or steal the global model without contribution. An attacker to the central agent can manipulate the model update to prevent the global model from converging.  

Authors: What are the challenges in defining and comparing threat models for privacy-preserving federated learning?

Dr. Xiaowei Huang and Dr. Yi Dong, University of Liverpool:  Even for a well-discussed attack such as poisoning attack, due to its distributed nature and privacy constraints, there might be different threat models (e.g., noisy, observational, or Byzantine attackers).  

To enable a rigorous study, a threat model needs to be well-articulated. However, a formal model that can describe different assumptions is still missing. This state of the art has made the comparison between methods (either learning or defense) hard.

The Theory-Reality Gap

Research on privacy-preserving federated learning often makes simplifying assumptions that are not reasonable in real-world deployments. These gaps between theory and practice remain a barrier to developing deployable PPFL systems, and most existing systems have filled these gaps with custom solutions. In addition to limiting the potential for PPFL systems to be adoptable on a wider scale, this approach also means that it’s difficult to ensure that deployed PPFL systems are reliable and free of bugs. This challenge is compounded by the need for real-world PPFL systems to integrate with existing data infrastructure—a requirement that can also lead to important security and privacy problems. Several participants in the UK-US PETs Prize Challenges highlighted issues relating to this.

Authors: What major gaps still exist between the theory and practice of privacy-preserving federated learning?

Dr. Xiaowei Huang and Dr. Yi Dong, University of Liverpool:  Current federated learning (FL) or PPFL focus on algorithmic development, by abstracting away some real-world settings on which the FL or PPFL algorithm will run. For example, it may not consider the cases where some or all local agents do not have sufficient computational powers or memory to conduct large scale training and inference, and it may not consider the open environment in which there are eavesdropper or attacker to compromise security or privacy properties of the algorithms.

Dr. Mat Weldon, UK Office for National Statistics (ONS), Data Science Campus:  The problem with the current, highly bespoke, federated learning solutions is that there are so many moving parts, and every moving part needs to be independently threat tested for each new solution. It’s easier to design a new federated learning architecture than it is to red team it.

The discipline is currently in a very fluid state – every new solution is bespoke and tailored to a particular engineering problem. This makes it difficult to achieve economies of scale. I predict that over the next few years we’ll see protocols emerge that crystallize common patterns, in the same way that cryptographic protocols emerged and crystallized web commerce.

Dr. Michael Fenton, Trūata:  In the majority of solutions that we have observed, small but critical flaws in the overall system design can lead to privacy breaches. These flaws typically arise because solution designers often seek to retrofit existing legacy solutions or systems to add privacy-preserving elements as a time and cost-saving measure. The net result is that the overall system becomes poorly optimized for privacy protection since in many cases an optimal solution may necessitate starting from scratch which can be prohibitively expensive from a development perspective.  Privacy-by-design means building privacy protections into a system on paper and in practice (i.e. both designing a system to be privacy-preserving from the ground up and testing the entire system to ensure those privacy protections are having the desired effect).

Meeting the Challenge

The challenges described in this post are associated with the early stage of development for PPFL systems—a situation that many working in this area hope will improve with time. 

As organizations begin building and deploying PPFL systems, we are learning more about processes for threat modeling. For example, it’s important to carefully articulate the most important security and privacy risks of the deployment context and ensure that the threat model includes all the attacker capabilities associated with these risks.

Growing interest in practical deployments is also driving the development of flexible software tools. Open-source software frameworks like Flower ,  PySyft ,  FATE , and  TensorFlow Federated are fast becoming more mature and capable, and collaborative efforts like the  UN PET Lab , the  National Secure Data Service , and challenges like the  UK-US PETs Prize Challenge are continuing to raise awareness about the need for these technologies.

Coming Up Next

Solutions for privacy-preserving federated learning combine distributed systems with complex privacy techniques, resulting in unique scalability challenges. In our next post, we’ll discuss these challenges and some of the emerging ideas for addressing them.

About the author

Joseph Near

Joseph Near is an assistant professor of computer science at the University of Vermont who supports NIST as a moderator for the Privacy Engineering Collaboration Space. His research interests include data privacy, computer security, and programming languages. Joseph received his B.S. in computer science from Indiana University, and his M.S. and Ph.D. in computer science from MIT.

David Darais

David Darais is a Principal Scientist at Galois, Inc. and supports NIST as a moderator for the Privacy Engineering Collaboration Space. David's research focuses on tools for achieving reliable software in critical, security-sensitive, and privacy-sensitive systems. David received his B.S. from the University of Utah, M.S. from Harvard University and Ph.D. from the University of Maryland.

Mark Durkee

Mark Durkee is Head of Data & Technology at the Centre for Data Ethics and Innovation (CDEI). He leads a portfolio of work including the CDEI's work on the Algorithmic Transparency Recording Standard, privacy enhancing technologies, and a broader programme of work focused on promoting responsible access to data. He previously led CDEI's independent review into bias in algorithmic decision-making. He has spent over a decade working in a variety of technology strategy, architecture and cyber security roles within the UK government, and previously worked as a software engineer and completed a PhD in Theoretical Physics.

Related posts

Protecting trained models in privacy-preserving federated learning, nist’s international cybersecurity and privacy engagement update – mexico city, rsa conference, and more, latest nice framework update offers improvements for the cybersecurity workforce, add new comment.

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Eaia: an efficient and anonymous identity-authentication scheme in 5g-v2v.

1. Introduction

• In the mutual authentication between vehicles process, the proposed protocol achieves authentication and session key negotiation without the involvement of TAs and RSUs, enabling vehicles to communicate in scenarios lacking traffic infrastructure.
• Using temporary anonymous identities, nodes cannot resolve each other’s real identities, thereby protecting privacy. Once the authentication session is initiated, the established temporary session key is used, avoiding the burden of key management and making it difficult for attackers to obtain keys or tamper with messages.
• Considering the limited computational resources of vehicles, the authentication protocol is designed to be lightweight and efficient while resisting various complex typical attacks.

2. Related Work

3. preliminaries, 3.1. elliptic curve cryptosystem, 3.2. mathematical problems.

• Elliptic Curve Discrete Logarithm Problem (ECDLP) The ECDLP is the foundation of elliptic curve cryptography. Given an elliptic curve E and two points P and Q on it, if there exists an integer k such that Q = k P , then k is the discrete logarithm of Q with respect to P . Computing this k is known as solving the ECDLP. This problem is considered very difficult, especially over large prime fields, providing the security basis for elliptic curve cryptography.
• Elliptic-Curve Diffie–Hellman (ECDH) ECDH is a key-exchange protocol based on elliptic curves. It allows two participants, who do not share any prior secret information, to agree on a shared key over an insecure communication channel. The steps are as follows: Step 1 Key Generation: each participant chooses a private key a and b and computes the corresponding public keys A = a P and B = b P , where P is a generator on the elliptic curve. Step 2 Key exchange: participants exchange their public keys. Step 3 Shared Key Computation: Each participant uses the other’s public key and their own private key to compute the shared key. The first participant computes S = a B , and the second participant computes S ′ = b A . Since S = S ′ = a b P , both participants arrive at the same shared key.

3.3. Certificate-Less Public Key Cryptography (CL-PKC)

4. system model, 4.1. system model, 4.2. attack model.

• Eavesdropping, Interception, Modification, or Deletion of Messages: An adversary can eavesdrop on, intercept, modify, or delete publicly transmitted messages, potentially compromising the confidentiality and integrity of the communication. Passive attacks may also be used to gather sensitive information.
• Replay Attacks: an adversary might capture and resend previously transmitted data packets to deceive other vehicles or infrastructure, leading to the propagation of duplicate or misleading information.
• Message or credential forgery: an adversary might forge false messages or credentials to impersonate legitimate vehicles or road infrastructure, causing the dissemination of incorrect traffic information or false warning messages, thereby impacting road safety.
• Man-in-the-middle attacks: an adversary could position themselves between communicating parties, establishing normal connections with both sides and deceiving them into exchanging data through the attacker.

5. Proposed Scheme EAIA

5.1. system initialization, 5.2. registration, 5.3. mutual authentication, 5.4. pseudoidentity update, 6. security evaluation, 6.1. security analysis.

• Mutual authentication: For two vehicles requiring mutual authentication, O B U i encrypts its identity using O B U j ’s public key, ensuring that only O B U j can extract O B U i ’s identity. To validate the signature and verify the validity of O B U i , O B U j uses its private key to compute M ′ . Only the target vehicle O B U j can obtain the correct identity and random number A of O B U i and verify O B U i ’s identity. Therefore, O B U i can also validate the validity of O B U j .
• Secure session key agreement: The integrity and confidentiality of the session key are ensured by the principles of ECCDH. If an adversary could forge a session key between vehicles, it would imply that the adversary could solve the computational Diffie–Hellman problem, which is known to be difficult, as discussed in Section 3.2 .
• Anonymity and privacy protection: In the proposed protocol, real identities are anonymized by generating pseudonyms, which are then obscured by hash functions. During the authentication process, the messages { B , N , σ , T a } and { D , η , T b } do not directly transmit identities. Instead, identities are linked with random numbers, preventing the sender’s identity from being disclosed. Thus, the proposed protocol satisfies user anonymity and privacy protection requirements.
• Resistance to man-in-the-middle attacks: During authentication, authenticated OBUs can verify the requesting OBU by generating its signature σ using the requesting vehicle’s private key x i + y i . Without this private key, the authenticated vehicle cannot extract the identity of the requesting vehicle. If an adversary attempts a man-in-the-middle attack, they must possess x i + y i to complete identity authentication and key exchange. However, x i + y i remains unknown to any adversary.
• Resistance to impersonation attacks: To successfully impersonate a vehicle, an attacker needs to know the private key x i + y i of the requesting OBU to generate a legitimate signature σ . Since the attacker cannot obtain the private key x i + y i of the requesting vehicle, they cannot generate a valid signature, thus preventing impersonation.
• Resistance to Replay Attacks: in the proposed protocol, timestamps T a and T b ensure that session keys cannot be reused by adversaries to disrupt the mutual authentication process.
• Perfect forward secrecy: Forward secrecy ensures that even if participants’ long-term private keys and previous session keys are compromised, the current session key remains secure. In the proposed protocol, if the private keys x i + y i and x j + y j of two participants are leaked, adversaries still cannot access the session key without knowing the temporary keys. Assuming the current session keys are S K j − i = h 3 I D i ′ I D j d k A ′ + X i and S K i − j = h 3 I D i I D j D k a + X i , adversaries might access I D i and I D j . For d k A ′ + X i , it should be computed as d k a + x i P , where k = h 1 ( I D i | | I D j | | A | | D | | T b ) . However, adversaries do not have access to the temporary keys d or a involved in generating the session key. Therefore, our protocol meets the requirements for forward secrecy.
• Resistance to Random Number Leakage: during the authentication process, even if the random numbers a , b , and d are leaked, adversaries cannot generate the correct session key because the secret keys of the vehicles are used as part of the session key.

6.2. Formal Proof by BAN Logic

• Goal 1: O B U i | ≡ ( Y i , y i )
• Goal 2: O B U i | ≡ O B U i ⟷ S K O B U j
• Goal 3: O B U i ≡ O B U j ≡ O B U i ⟷ S K O B U j
• Goal 4: O B U j | ≡ O B U i ⟷ S K O B U j
• Goal 5: O B U j | ≡ O B U i | ≡ O B U i ⟷ S K O B U j
• Message 1: O B U i → A M F : { R I D , X i }
• Message 2: A M F → O B U i : { y i , Y i , I D , R }
• Message 3: O B U i → O B U j : { B , N , σ , T a }
• Message 4: O B U j → O B U i : { D , η , T b }
• A 1 : O B U i | ≡ → p k A M F
• A 2 : O B U i | ≡ # ( X i , Y i )
• A 3 : O B U i | ≡ A M F ⟹ ( X i , Y i )
• A 4 : O B U j | ≡ ⟶ X i + Y i O B U i
• A 5 : O B U i | ≡ ⟶ X j + Y j O B U j
• A 6 : O B U j ≡ # ( T a , O B U j ≡ # ( T b
• A 7 : O B U i ≡ # ( T a , O B U i ≡ # ( T b
• A 8 : O B U j | ≡ O B U i ⟹ O B U i ⟷ S K O B U j
• A 9 : O B U i | ≡ O B U j ⟹ O B U i ⟷ S K O B U j

6.3. Formal Verification by Scyther Tool

7. performance evaluation, 7.1. computation cost, 7.2. communication cost, 7.3. energy consumption, 7.4. discussion, 8. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Share and Cite

Du, Q.; Zhou, J.; Ma, M. EAIA: An Efficient and Anonymous Identity-Authentication Scheme in 5G-V2V. Sensors 2024 , 24 , 5376. https://doi.org/10.3390/s24165376

Du Q, Zhou J, Ma M. EAIA: An Efficient and Anonymous Identity-Authentication Scheme in 5G-V2V. Sensors . 2024; 24(16):5376. https://doi.org/10.3390/s24165376

Du, Qianmin, Jianhong Zhou, and Maode Ma. 2024. "EAIA: An Efficient and Anonymous Identity-Authentication Scheme in 5G-V2V" Sensors 24, no. 16: 5376. https://doi.org/10.3390/s24165376

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