Factoring via Superencyrption

Berkovits, Shimshon

doi:10.1080/0161-118291857028

Cited by 6 publications

(3 citation statements)

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“…In this section, we give a different reduction for Theorem 4.1 (Note that Theorem 4.2 is an equivalent restatement of Theorem 4.1). The high-level idea is that an efficient low order adversary would be able to efficiently launch the generalized cycling attack [SN77,Ber82] to factor RSA moduli such that φ(N ) has no prime factor between a constant B (or equivalently a polynomial of λ) and 2 log 1+ (λ) , for > 0 and gcd(p − 1, q − 1) = 2.…”

Section: 2mentioning

confidence: 99%

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A note on Low Order assumptions in RSA groups

Seres

Burcsi

2021

Rad Hrvatske akademije znanosti i umjetnosti

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In this short note, we show that substantially weaker Low Order assumptions are sufficient to prove the soundness of Pietrzak's protocol for proof of exponentiation in groups of unknown order. This constitutes the first step to a better understanding of the asymptotic computational complexity of breaking the soundness of the protocol. Furthermore, we prove the equivalence of the (weaker) Low Order assumption(s) and the Factoring assumption in RSA groups for a non-negligible portion of moduli. We argue that in practice our reduction applies for a considerable amount of deployed moduli. Our results have cryptographic applications, most importantly in the theory of recently proposed verifiable delay function constructions. Finally, we describe how to certify RSA moduli free of low order elements.

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Section: 2mentioning

confidence: 99%

“…By our assumption, adversary A with non-negligible probability outputs a pair (u, l), i.e. a low order element u with order l. In the following, we will take advantage of the generalized cycling attack on RSA groups [Ber82].…”

Section: 2mentioning

confidence: 99%

A note on Low Order assumptions in RSA groups

Seres

Burcsi

2021

Rad Hrvatske akademije znanosti i umjetnosti

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“…To guarantee cryptographical security the prime factors of the parameter n should be strong primes. For more information see (Rivest, Shamir and Adleman, 1978), (Berkovits, 1982), (Gordon, 1984) and (Jamnig, 1984). We can make the system more practicable by choosing the message M from Zp, where p := milli{p;} instead of Z~.…”

Section: Lemmamentioning

confidence: 99%

Power permutations on prime residue classes

Harald

Christian

1995

IFIP Advances in Information and Communication Technology

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Nobauer proofed in (Nobauer, 1954) that the power function x f--7 xk mod n is a permutation on Zn for a positive integer n iff n is squarefree and (k, .\(n)) = 1, where .\(n) denotes the Carmichael function and (a, b) the greatest common divisor of a and b. The RSA-cryptosystem uses this property for n = pq, where p, q are distinct primes. Hence the modul cannot be chosen arbitrarily. If we consider permutations on prime residue classes, there is no restriction for the module anymore. In order to find criteria for power permutations on Z~ we first deal with the fixed point problem. As a consequence we get the condition for k : r (k,[cfJ(p~', ... ,p~"])=1 for n=IJpf', i=l where q, denotes the Euler totient function and [a, b] the least common multiple of a and b.

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Cryptanalysis of the Dickson-Scheme

Müller

Nöbauer

Advances in Cryptology — EUROCRYPT’ 85

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Factoring via Superencyrption

Cited by 6 publications

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A note on Low Order assumptions in RSA groups

A note on Low Order assumptions in RSA groups

Power permutations on prime residue classes

Cryptanalysis of the Dickson-Scheme

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