New Attacks on the RSA Cryptosystem

Nitaj, Abderrahmane; Ariffin, Muhammad Rezal Kamel; Nassr, Dieaa I.; Bahig, Hatem M.

doi:10.1007/978-3-319-06734-6_12

Cited by 25 publications

(21 citation statements)

References 16 publications

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“…From our result, one can observe that we get d ≈ N 0.3706 , which is larger than Blömer-May's bound x < 1 3 N 0.25 , as reported in Reference [12]. Our d ≈ N 0.3706 is also larger than Nitaj et al's bound d ≈ N 0.344 , as reported in Reference [13] .…”

Section: Examplecontrasting

confidence: 44%

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New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method

et al. 2018

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This paper presents new short decryption exponent attacks on RSA, which successfully leads to the factorization of RSA modulus N = pq in polynomial time. The paper has two parts. In the first part, we report the usage of the small prime difference method of the form |b 2 p − a 2 q| < N γ where the ratio of. The second part of the paper reports four cryptanalytic attacks on t instances of RSA moduli N s = p s q s for s = 1, 2, . . . , t where we use N − a 2 +b 2 ab √ N + 1 as an approximation of φ(N) satisfying generalized key equations of the shape e s d s for unknown positive integers d, k s , d s , k s , and z s , where we establish that t RSA moduli can be simultaneously factored in polynomial time using combinations of simultaneous Diophantine approximations and lattice basis reduction methods. In all the reported attacks, we have found an improved short secret exponent bound, which is considered to be better than some bounds as reported in the literature.

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Section: Examplecontrasting

confidence: 44%

“…, N t in polynomial time. We have found decryption exponents bounds that are greater than those of References [12,13].…”

Section: Introductionmentioning

confidence: 63%

New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method

et al. 2018

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“…The ways in which RSA might be attacked are well studied and 20 years ago the attacks were well catalogued [8]. The intervening years has seen new forms of attack reported [9] but the problem is always the efficiency with which we can implement these factoring algorithms on conventional computers.…”

Section: Factoring Algorithmsmentioning

confidence: 99%

Will quantum computers be the end of public key encryption?

Buchanan

Woodward

2016

Journal of Cyber Security Technology

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The emergence of practical quantum computers poses a significant threat to the most popular public key cryptographic schemes in current use. While we know that the well-understood algorithms for factoring large composites and solving the discrete logarithm problem run at best in superpolynomial time on conventional computers, new, less well understood algorithms run in polynomial time on certain quantum computer architectures. Many appear to be heralding this next step in computing as 'the end of public key encryption'. We argue that this is not the case and that there are many fields of mathematics that can be used for creating 'quantum resistant' cryptographic schemes. We present a high-level review of the threat posed by quantum computers, using RSA and Shor's algorithm as an example but we explain why we feel that the range of quantum algorithms that pose a threat to public key encryption schemes is likely to be limited in future. We discuss some of the other schemes that we believe could form the basis for public key encryption schemes, some of which could enter widespread use in the very near future, and indicate why some are more likely to be adopted.

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“…Extending the result from [16], this paper presents an attack on the modulus N = p 2 q when the primes share a known amount of the LSBs while d 1 and d 2 share an amount of their MSBs. We formulate a lemma by ulitizing the information on the sharing LSBs between the primes.…”

Section: Introductionmentioning

confidence: 97%

“…Sun et al [14] and Zhao et al [15] also showed that using primes that share either most or least significant bits are insecure and the modulus can be factored in polynomial time. Following through in 2014, Nitaj et al [16] came out with an idea to attack the modulus N = pq where the primes share their LSBs and there exists two public parameters e 1 and e 2 such that the corresponding decryption parameters d 1 and d 2 share their MSBs. They showed that if the RSA crytosystem satisfies those conditions, then it is possible to factor N provided…”

Section: Introductionmentioning

confidence: 99%

New Jochemsz–May Cryptanalytic Bound for RSA System Utilizing Common Modulus N = p2q

et al. 2021

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This paper describes an attack on the Rivest, Shamir and Adleman (RSA) cryptosystem utilizing the modulus N=p2q where p and q are two large balanced primes. Let e1,e2<Nγ be the integers such that d1,d2<Nδ be their multiplicative inverses. Based on the two key equations e1d1−k1ϕ(N)=1 and e2d2−k2ϕ(N)=1 where ϕ(N)=p(p−1)(q−1), our attack works when the primes share a known amount of least significant bits (LSBs) and the private exponents share an amount of most significant bits (MSBs). We apply the extended strategy of Jochemsz–May to find the small roots of an integer polynomial and show that N can be factored if δ<1110+94α−12β−12γ−130180γ+990α−180β+64. Our attack improves the bounds of some previously proposed attacks that makes the RSA variant vulnerable.

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New Attacks on the RSA Cryptosystem

Cited by 25 publications

References 16 publications

New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method

New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method

Will quantum computers be the end of public key encryption?

New Jochemsz–May Cryptanalytic Bound for RSA System Utilizing Common Modulus N = p2q

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