A Generalized Takagi-Cryptosystem with a Modulus of the Form prqs

Lim, So Yeon; Kim, Seungjoo; Yie, Ikkwon; Lee, Hongsub

doi:10.1007/3-540-44495-5_25

Cited by 22 publications

(20 citation statements)

References 3 publications

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“…In that case the condition for polynomial-time factorization becomes r = Ω(log Q) = Ω(log p), the same condition as BDH. This shows that N = p r+1 q r can also be factored in polynomial time for large r. We note that in [LKYL00] only moduli of the form N = p r+1 q r were considered for lattice-based factorisation.…”

Section: Introductionmentioning

confidence: 88%

“…In light of the BDH attack, Takagi's cryptosystem was later extended by Lim et al in [LKYL00] to moduli of the form N = p r q s . Namely the authors describe a public-key cryptosystem with modulus N = p r q s , and obtain even faster decryption than in Takagi's cryptosystem.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore one could be tempted to use the Lim et al cryptosystem [LKYL00], since no attack is known and it offers a significant speed-up compared to standard RSA. In this paper we show that moduli of the form N = p r q s can also be factored in polynomial time for large r and/or s; this gives a new class of integers that can be factored efficiently.…”

Section: Introductionmentioning

confidence: 99%

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Factoring $$N=p^rq^s$$ for Large r and s

Coron

Faugère

Renault

et al. 2016

Topics in Cryptology - CT-RSA 2016

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Factoring $$N=p^rq^s$$ for Large r and s

Coron

Faugère

Renault

et al. 2016

Topics in Cryptology - CT-RSA 2016

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“…About at the same time Takagi [5] proposed an even faster solution using the modulus N = p r q, for which the exponentiation modulo p r is computed using the Hensel lifting method [6, p.137]. Later, this solution has been generalized to the modulus N = p r q s [7]. According to [3] the appropriate number of primes to be chosen in order to resist state-of-the-art factorization algorithms depends from the modulus size, and, precisely, it can be: up to 3 primes for 1024, 1536, 2048, 2560, 3072, and 3584 bit modulus, up to 4 for 4096, and up to 5 for 8192.…”

Section: Multifactor Rsamentioning

confidence: 99%

A Multi-factor RSA-like Scheme with Fast Decryption Based on Rédei Rational Functions over the Pell Hyperbola

Bellini

Murru

2020

Lecture Notes in Computer Science

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We propose a generalization of an RSA-like scheme based on Rédei rational functions over the Pell hyperbola. Instead of a modulus which is a product of two primes, we define the scheme on a multi-factor modulus, i.e. on a product of more than two primes. This results in a scheme with a decryption which is quadratically faster, in the number of primes factoring the modulus, than the original RSA, while preserving a better security. The scheme reaches its best efficiency advantage over RSA for high security levels, since in these cases the modulus can contain more primes. Compared to the analog schemes based on elliptic curves, as the KMOV cryptosystem, the proposed scheme is more efficient. Furthermore a variation of the scheme with larger ciphertext size does not suffer of impossible group operation attacks, as it happens for schemes based on elliptic curves.

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“…In order to gain a faster decryption, Takagi [27] variant of RSA with a modulus n = p r q. For similar reasons, Lim et al [17] presented a variant of RSA and Takagi schemes with a modulus n = p r q s . Such variants are used in cryptography for various applications such as electronic cash [6] and the design of Okamoto-Uchiyama scheme [22].…”

Section: Introductionmentioning

confidence: 97%