A new attack on some RSA variants

Nitaj, Abderrahmane; Susilo, Willy; Tonien, Joseph

doi:10.1016/j.tcs.2023.113898

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…Micheli [18] provided relevant examples pertaining to key recovery in situations involving the partial leakage of information for these types of cryptographic problems. In recent years, the Coppersmith algorithm has remained one of the most important algorithms for analyzing RSA and its variants [19]. In addition, it has also been used to solve the sum of EC-HNP problems under certain conditions [20] and factorization problems when a sufficient number of bits of the prime factors are known [21].…”

Section: Introductionmentioning

confidence: 99%

An Improved Coppersmith Algorithm Based on Block Preprocessing

Zhang,

Qin,

Gao

et al. 2024

Mathematics

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Since Coppersmith proposed the use of the LLL algorithm to solve univariate modular polynomial equations at EUROCRYPT’96, it has sparked a fervent research interest in lattice analysis among cryptographers. Despite its polynomial-time nature, the LLL algorithm exhibits a high-order polynomial upper bound in terms of theoretical complexity, particularly with longer computation times when applied to high-dimensional lattices. In addressing this issue, we propose an improved algorithm based on block preprocessing, building on the original Coppersmith algorithm and thus providing proof of correctness for this algorithm. This approach effectively reduces the solution time of the algorithm, offering a maximum improvement of 8.1% compared to the original Coppersmith algorithm. Additionally, we demonstrate the compatibility of our algorithm with the rounding algorithm proposed at PKC 2014. The combined utilization of these approaches further enhances the efficiency of our algorithm. The experimental results show that the combined algorithm achieves a maximum improvement of 22.4% in solution time compared to the original Coppersmith algorithm. It also outperforms the standalone rounding algorithm with a maximum improvement of 12.1%. When compared to the improved Coppersmith algorithm based on row common factor extraction, our proposed algorithm demonstrates comparable or even superior performance in certain dimensions. The block preprocessing algorithm in our approach enables independent execution without data exchange, making it suitable for leveraging multi-processing advantages in scenarios involving higher degrees of modular polynomial equations. This offers a new perspective for achieving the parallel computation of the Coppersmith algorithm, facilitating parallel execution and providing valuable insights.

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Section: Introductionmentioning

confidence: 99%

An Improved Coppersmith Algorithm Based on Block Preprocessing

Zhang,

Qin,

Gao

et al. 2024

Mathematics

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An Improved Public Key Cryptographic Algorithm Based on Chebyshev Polynomials and RSA

Zhang,

Liang,

Tavares

et al. 2024

Symmetry

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Due to its very desirable properties, Chebyshev polynomials are often used in the design of public key cryptographic systems. This paper discretizes the Chebyshev mapping, generalizes the properties of Chebyshev polynomials, and proposes an improved public key encryption algorithm based on Chebyshev chaotic mapping and RSA, i.e., CRPKC−Ki. This algorithm introduces alternative multiplication coefficients Ki, the selection of which is determined by the size of TrTdxmod N=TdTrxmod N, and the specific value selection rules are shared secrets among participants, overcoming the shortcomings of previous schemes. In the key generation and encryption/decryption stages, more complex intermediate processes are used to achieve higher algorithm complexity, making the algorithm more robust against ordinary attacks. The algorithm is also compared with other RSA-based algorithms to demonstrate its effectiveness in terms of performance and security.

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A new attack on some RSA variants

Cited by 2 publications

References 23 publications

An Improved Coppersmith Algorithm Based on Block Preprocessing

An Improved Coppersmith Algorithm Based on Block Preprocessing

An Improved Public Key Cryptographic Algorithm Based on Chebyshev Polynomials and RSA

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