Sampling from Signed Quadratic Residues: RSA Group Is Pseudofree

Jhanwar, Mahabir Prasad; Barua, Rana

doi:10.1007/978-3-642-10628-6_16

Cited by 7 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore the above result of Micciancio remains valid if we replace Sn by On in it. The same result as in [22], but with slightly different representations of group elements by bit strings and different distributions of random elements of the groups, was obtained by Jhanwar and Barua [20]. Moreover, Catalano, Fiore, and Warinschi [9] proved that under the same assumption as in the above result of Micciancio, the family ((Z * n , U(Sn)) | n ∈ S) satisfies an apparently stronger condition than pseudo-freeness in A.…”

Section: Related Worksupporting

confidence: 65%

“…Indeed, this holds if and only if there are infinitely many Sophie Germain primes, which is a well-known unproven conjecture in number theory. Thus, the assumption used in [9,20,22] is very strong.…”

Section: Related Workmentioning

confidence: 99%

“…In this subsection, we assume that H is a family of computational Ω-algebras in V. We consider (weak) s-pseudo-freeness only when s is a constant. Note that in many works (see, e.g., [19,20,22,26,27]), pseudo-freeness (resp., weak pseudo-freeness) is understood as 1-pseudo-freeness (resp., weak 1-pseudo-freeness). It is evident that any pseudo-free (resp., weakly pseudo-free) family of computational Ω-algebras in V with respect to D and σ is also s-pseudo-free (resp., weakly s-pseudo-free) in V with respect to D and σ. Rivest remarked that in the variety of all groups, 1-pseudo-freeness is equivalent to pseudo-freeness (see [26,Subsection 5.1]).…”

Section: (Weakly) Pseudo-free Families Of Computational ω-Algebrasmentioning

confidence: 99%

See 2 more Smart Citations

Pseudo-free families of computational universal algebras

Anokhin¹

2020

Journal of Mathematical Cryptology

View full text Add to dashboard Cite

Let Ω be a finite set of finitary operation symbols. We initiate the study of (weakly) pseudo-free families of computational Ω-algebras in arbitrary varieties of Ω-algebras. A family (Hd | d ∈ D) of computational Ω-algebras (where D ⊆ {0, 1}*) is called polynomially bounded (resp., having exponential size) if there exists a polynomial η such that for all d ∈ D, the length of any representation of every h ∈ Hd is at most $\eta (|d|)\left( \text{ resp}\text{., }\left| {{H}_{d}} \right|\le {{2}^{\eta (|d|)}} \right).$First, we prove the following trichotomy: (i) if consists of nullary operation symbols only, then there exists a polynomially bounded pseudo-free family; (ii) if Ω = Ω0 ∪ {ω}, where 0 consists of nullary operation symbols and the arity of ω is 1, then there exist an exponential-size pseudo-free family and a polynomially bounded weakly pseudo-free family; (iii) in all other cases, the existence of polynomially bounded weakly pseudo-free families implies the existence of collision-resistant families of hash functions. In this trichotomy, (weak) pseudo-freeness is meant in the variety of all Ω-algebras. Second, assuming the existence of collision-resistant families of hash functions, we construct a polynomially bounded weakly pseudo-free family and an exponential-size pseudo-free family in the variety of all m-ary groupoids, where m is an arbitrary positive integer.

show abstract

Section: Related Worksupporting

confidence: 65%

Section: Related Workmentioning

confidence: 99%