Abderrahmane Nitaj’s research while affiliated with French National Centre for Scientific Research and other places

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Publications (81)


Figure 1. Single layer perceptron.
Figure 2. Multilayer perceptron.
Elliptic Curve Cryptography with Machine Learning
  • Article
  • Full-text available

December 2024

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111 Reads

Cryptography

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Abderrahmane Nitaj

Elliptic Curve Cryptography (ECC) is a technology based on the arithmetic of elliptic curves used to build strong and efficient cryptosystems and infrastructures. Several ECC systems, such as the Diffie–Hellman key exchange and the Elliptic Curve Digital Signature Algorithm, are deployed in real-life applications to enhance the security and efficiency of digital transactions. ECC has gained even more importance since the introduction of Bitcoin, the peer-to-peer electronic cash system, by Satoshi Nakamoto in 2008. In parallel, the integration of artificial intelligence, particularly machine learning, in various applications has increased the demand for robust cryptographic systems to ensure safety and security. In this paper, we present an overview of machine learning and Elliptic Curve Cryptography algorithms. We begin with a detailed review of the main ECC systems and evaluate their efficiency and security. Subsequently, we investigate potential applications of machine learning-based techniques to enhance the security and performance of ECC. This study includes the generation of optimal parameters for ECC systems using machine learning algorithms.

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Further cryptanalysis of some variants of the RSA cryptosystem

November 2024

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22 Reads

Journal of Applied Mathematics and Computing

To improve the security and the efficiency of the RSA cryptosystem, several variants have been proposed such as CRT-RSA, KMOV, Multiprime-RSA, Takagi-RSA, and Multiprime-power-RSA. Some variants use an RSA modulus N=pq with a public exponent e and a private exponent d satisfying ed1(mod(p21)(q21))ed\equiv 1\pmod {\left( p^2-1\right) \left( q^2-1\right) } or ed1(mod(p2+p+1)(q2+q+1))ed\equiv 1\pmod {\left( p^2+p+1\right) \left( q^2+q+1\right) }. In these variants, e is in the form e1d(mod(p21)(q21))e\equiv \frac{1}{d}\pmod {\left( p^2-1\right) \left( q^2-1\right) } or e1d(mod(p2+p+1)(q2+q+1))e\equiv \frac{1}{d}\pmod {\left( p^2+p+1\right) \left( q^2+q+1\right) } with a small d. In this paper, we present a new attack on the former variants whenever the public exponent e has the form ezu(mod(p21)(q21))e\equiv \frac{z}{u}\pmod {\left( p^2-1\right) \left( q^2-1\right) } or the form ezu(mod(p2+p+1)(q2+q+1))e\equiv \frac{z}{u}\pmod {\left( p^2+p+1\right) \left( q^2+q+1\right) } with small |z| and u. As a consequence, our class of weak exponents is much larger than the class in the former attacks. Our new method is based on Coppersmith’s method and lattice basis reduction, and breaks the variants in polynomial time when u and |z| are suitably small. Moreover, our method retrieves all the results of the former known attacks on such variants.


Small Public Exponent Brings More: Improved Partial Key Exposure Attacks against RSA

October 2024

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19 Reads

Let (N,e) be a public key of the RSA cryptosystem, and d be the corresponding private key. In practice, we usually choose a small e for quick encryption. In this paper, we improve partial private key exposure attacks against RSA with a small public exponent e. The key idea is that under such a setting we can usually obtain more information about the prime factor of N and then by solving a univariate modular polynomial with Coppersmith's method, N can be factored in polynomial time. Compared to previous results, we reduce the number of d's leaked bits needed to mount the attack by log_2 (e) bits. Furthermore, our experiments show that for 1024-bit N, our attack can achieve the theoretical bound on a personal computer, which verified our attack.


Partial Exposure Attacks on a New RSA Variant

October 2024

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29 Reads

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2 Citations

Cryptography

In 2022, Cotan and Teşeleanu presented a variant of the RSA cryptosystem where the modulus is of the form N=pq, and the private and the public exponents satisfy ed≡1(modψn(N)) with n≥2, and ψn(N)=pn−1qn−1(p−1)(q−1). This variant of RSA was recently cryptanalyzed by Nitaj, Adenan, and Ariffin at Africacrypt 2024. In this paper, we push further the cryptanalysis of the scheme of Cotan and Teşeleanu by presenting a method to solve the equation xH(y)+c≡0(mode) where c is a constant that is independent of x and y. This enables us to propose more attacks on the scheme, including a partial key exposure attack, an attack when the most significant bits of one of the prime factors are known, and an attack when the least significant bits of one of the prime factors are known.



Securing Data Exchange with Elliptic Curve Cryptography: A Novel Hash-Based Method for Message Mapping and Integrity Assurance

June 2024

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85 Reads

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4 Citations

Cryptography

To ensure the security of sensitive data, elliptic curve cryptography (ECC) is adopted as an asymmetric method that balances security and efficiency. Nevertheless, embedding messages into elliptic curve (EC) points poses a significant challenge. The intricacies of this process can greatly affect the overall security and efficiency of the cryptosystem, reflecting security vulnerabilities observed in many existing schemes that utilize ElGamal ECC-based encryption. In this paper, we introduce an innovative hash-based technique for securely embedding messages into EC points before encryption. A random parameter and a shared secret point generated through the EC Diffie–Hellman protocol are used to bolster the scheme’s security. The security of the proposed method is evaluated against various attack models; moreover, the complexity, and sensitivity of the encryption scheme, as well as its inputs, are analyzed. The randomness assessment of the ciphertext was performed using the NIST statistical test suite. Additionally, we propose a mechanism to ensure the integrity of the message by securely appending a tag to the ciphertext. As a consequence, a comprehensive analysis of our scheme demonstrates its effectiveness in maintaining data security and integrity against various attack models. The algorithm also meets more criteria such as the strict avalanche criterion, linear complexity, and operability.




A New Quantum-Resistant Electronic Voting Based on Fully Homomorphic Encryption

March 2024

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19 Reads

Lecture Notes in Electrical Engineering

The emergence of large quantum computers running Shor’s algorithm threatens the security of several cryptographic schemes in current use, including electronic voting. As a consequence, many post-quantum candidates that are quantum-resistant are actively investigated. Post-quantum schemes-based hard lattice problems are particularly promising. In this paper, we present and implement a new quantum-resistant electronic voting scheme and prove its efficiency and security by studying its algebraic complexity. Our scheme is based on a combination of two techniques: hard lattice problems and homomorphic encryption with Fan and Vercauteren system.


Generalized Implicit Factorization Problem

February 2024

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9 Reads

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3 Citations

Lecture Notes in Computer Science

The Implicit Factorization Problem (IFP) was first introduced by May and Ritzenhofen at PKC’09, which concerns the factorization of two RSA moduli N1=p1q1N_1=p_1q_1 and N2=p2q2N_2=p_2q_2, where p1p_1 and p2p_2 share a certain consecutive number of least significant bits. Since its introduction, many different variants of IFP have been considered, such as the cases where p1p_1 and p2p_2 share most significant bits or middle bits at the same positions. In this paper, we consider a more generalized case of IFP, in which the shared consecutive bits can be located at any positions in each prime, not necessarily required to be located at the same positions as before. We propose a lattice-based algorithm to solve this problem under specific conditions, and also provide some experimental results to verify our analysis.


Citations (42)


... In the era of expanding digital communication, the security of sensitive data is paramount, necessitating the continual advancement of encryption algorithms capable of resisting emerging cyber threats. Traditional encryption methods like Advanced Encryption Standard (AES) [4] and Rivest-Shamir-Adleman (RSA) [5], used to secure digital data, are increasingly vulnerable to sophisticated attacks. In response, research has increasingly explored alternative cryptographic foundations, including biologically inspired and computationally efficient models like cellular automata (CAs). ...

Reference:

Design of a Multi-Layer Symmetric Encryption System Using Reversible Cellular Automata
Partial Exposure Attacks on a New RSA Variant

Cryptography

... Note that for the RSA, a lattice approach that leads to a similar bound can be found in [30]. When n = 2, the optimal bounds presented in [31] for Elkamchouchi et al.'s scheme are identical with ours. Corollary 8. Let N = pq be the product of two unknown primes with q < p < 2q. ...

Cryptanalysis of a New Variant of the RSA Cryptosystem
  • Citing Chapter
  • July 2024

... Additionally, data availability and consistency are maintained across the distributed network by implementing robust synchronization protocols, preventing data loss and ensuring that all blockchain agents (B/As) operate with an up-to-date and uniform ledger. This approach reinforces the reliability of the system, even under high transaction loads or adverse network conditions [35]; 5. Preventive controls: To safeguard data and transactions from unauthorized access, cryptographic security measures are implemented within the blockchain framework. These include advanced encryption techniques, such as Elliptic Curve Cryptography (ECC) and AES-256, to ensure data confidentiality and integrity. ...

Securing Data Exchange with Elliptic Curve Cryptography: A Novel Hash-Based Method for Message Mapping and Integrity Assurance

Cryptography

... And their result is generally better than [NA15] when k > 3. In 2023, Feng et al. [FNP24] proposed a generalized IFP in which p 1 , p 2 share some bits at different positions. They successfully solved the problem using Coppersmith's method with the same technique for reducing the determinant of the lattice as [LPZ + 16], which yields a bound consistent with [WQLF17]. ...

Generalized Implicit Factorization Problem
  • Citing Chapter
  • February 2024

Lecture Notes in Computer Science

... In the context of cryptographic security, AI and ML are being employed to develop more resilient encryption schemes tailored to the resource constraints of IoT devices. For instance, AI-driven optimization techniques can be used to design lightweight cryptographic algorithms that balance security with computational efficiency [229][230][231]. Additionally, AI is being explored as a means to secure cryptographic keys through techniques such as quantum key distribution (QKD), where ML models are used to optimize key generation and distribution processes, enhancing the security of communication channels in IoT networks [232][233][234]. ...

Applications of Neural Network-Based AI in Cryptography

Cryptography

... There are multiple cryptographic characteristics that are available in literature to authenticate the applicability and robustness of an S-box. The most familiar cryptographic aspects of an S-box nonlinearity, strict avalanche criterion (SAC), bit independent criterion (BIC), linear approximation probability (LAP) and differential approximation probability (DAP) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. ...

Enhanced S-boxes for the Advanced Encryption Standard with maximal periodicity and better avalanche property
  • Citing Article
  • June 2023

Computer Standards & Interfaces

... In addition, side-channel attack (SCA) is also an important threat to RSA [3,4,7,8,23,29], where the main objective is to obtain more information about the private key by collecting electromagnetic information during the operation of the encryption software or hardware. The security analysis of some variants of RSA [18,35,36] has also received the favor of researchers. Such in-depth analyses have laid a secure foundation for the safe use of the RSA system. ...

A new attack on some RSA variants
  • Citing Article
  • April 2023

Theoretical Computer Science

... They pointed out that successful implicit factorization of two RSA moduli is achievable when t > 2α − 2α 2 . Further improvements on the generalized implicit factorization problem were presented in (Wang et al. 2021;Feng et al. 2023) and cryptanalysis of RSA with implicitly related keys was studied by Zheng et al. (2020). ...

Generalized Implicit Factorization Problem

... This signifies recent advancements exploring more attacks on RSA-type cryptosystems using the lattice-based method, coupled with improvements in lattice construction to enhance attack Fig. 7 The keyword co-occurrence network map in lattice-based cryptanalysis of RSA-type cryptosystems efficiency. It is worth noting that the latest cryptanalysis such as (Zheng et al. 2021;Shi et al. 2022;Nitaj et al. 2022) is centered around the RSA variant using Pell equation (Murru and Saettone 2017). ...

Security Issues of Novel RSA Variant

IEEE Access

Abderrahmane Nitaj

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