scholarly journals An Attack Bound for Small Multiplicative Inverse of φ(N) mod e with a Composed Prime Sum p+q Using Sublattice Based Techniques

Cryptography ◽  
2018 ◽  
Vol 2 (4) ◽  
pp. 36 ◽  
Author(s):  
Pratha Anuradha Kameswari ◽  
Lambadi Jyotsna
Keyword(s):  
Positive Integer ◽  
Polynomial Equations ◽  
Multiplicative Inverse ◽  
Reduction Techniques ◽  
Small Roots ◽  
Modular Polynomial ◽  
Lattice Dimension

In this paper, we gave an attack on RSA (Rivest–Shamir–Adleman) Cryptosystem when φ(N) has small multiplicative inverse modulo e and the prime sum p + q is of the form p + q = 2nk0 + k1, where n is a given positive integer and k0 and k1 are two suitably small unknown integers using sublattice reduction techniques and Coppersmith’s methods for finding small roots of modular polynomial equations. When we compare this method with an approach using lattice based techniques, this procedure slightly improves the bound and reduces the lattice dimension. Employing the previous tools, we provide a new attack bound for the deciphering exponent when the prime sum p + q = 2nk0 + k1 and performed an analysis with Boneh and Durfee’s deciphering exponent bound for appropriately small k0 and k1.

scholarly journals An Attack Bound for Small Multiplicative Inverse of Euler function of modulo "e" with a Composed Prime Sum p+q Using Sublattice Based Techniques

2018 ◽  
Author(s):  
Anuradha Kameswari Pratha ◽  
Jyotsna Lambadi
Keyword(s):  
Positive Integer ◽  
Polynomial Equations ◽  
Multiplicative Inverse ◽  
Euler Function ◽  
Reduction Techniques ◽  
Small Roots ◽  
Modular Polynomial ◽  
Lattice Dimension

In this paper, we gave an attack on RSA when Euler function has small multiplicative inverse modulo "e" and the prime sum p+q is of the form p+q=2^nk_0+k_1 where n is a given positive integer and k_0 and k_1 are two suitably small unknown integers using sublattice reduction techniques and Coppersmith's methods for finding small roots of modular polynomial equations. When we compare this method with an approach using lattice based techniques, this procedure slightly improves the bound and reduces the lattice dimension.

Solving a class of modular polynomial equations and its relation to modular inversion hidden number problem and inversive congruential generator

2017 ◽  
Vol 86 (9) ◽  
pp. 1997-2033 ◽  
Author(s):  
Jun Xu ◽  
Santanu Sarkar ◽  
Lei Hu ◽  
Zhangjie Huang ◽  
Liqiang Peng
Keyword(s):  
Polynomial Equations ◽  
Congruential Generator ◽  
Number Problem ◽  
Hidden Number Problem ◽  
Modular Polynomial ◽  
Modular Inversion

scholarly journals Analytical cryptanalysis upon N = p2q utilizing Jochemsz-May strategy

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248888
Author(s):  
Nurul Nur Hanisah Adenan ◽  
Muhammad Rezal Kamel Ariffin ◽  
Faridah Yunos ◽  
Siti Hasana Sapar ◽  
Muhammad Asyraf Asbullah
Keyword(s):  
Multiplicative Inverse ◽  
Small Roots ◽  
Image Position ◽  
Integer Polynomial ◽  
Least Significant Bits

This paper presents a cryptanalytic approach on the variants of the RSA which utilizes the modulus N = p2q where p and q are balanced large primes. Suppose e∈Z+ satisfying gcd(e, ϕ(N)) = 1 where ϕ(N) = p(p − 1)(q − 1) and d < Nδ be its multiplicative inverse. From ed − kϕ(N) = 1, by utilizing the extended strategy of Jochemsz and May, our attack works when the primes share a known amount of Least Significant Bits(LSBs). This is achievable since we obtain the small roots of our specially constructed integer polynomial which leads to the factorization of N. More specifically we show that N can be factored when the bound δ<119−294+18γ. Our attack enhances the bound of some former attacks upon N = p2q.

Catalogue reduction techniques

1978 ◽  
Vol 48 ◽  
pp. 389-390 ◽  
Author(s):  
Chr. de Vegt
Keyword(s):  
Adjustment Process ◽  
Proper Motions ◽  
Measuring Process ◽  
Aerial Photogrammetry ◽  
Reduction Techniques ◽  
Observational Technique ◽  
The Common ◽  
Astrometric Data

AbstractReduction techniques as applied to astrometric data material tend to split up traditionally into at least two different classes according to the observational technique used, namely transit circle observations and photographic observations. Although it is not realized fully in practice at present, the application of a blockadjustment technique for all kind of catalogue reductions is suggested. The term blockadjustment shall denote in this context the common adjustment of the principal unknowns which are the positions, proper motions and certain reduction parameters modelling the systematic properties of the observational process. Especially for old epoch catalogue data we frequently meet the situation that no independent detailed information on the telescope properties and other instrumental parameters, describing for example the measuring process, is available from special calibration observations or measurements; therefore the adjustment process should be highly self-calibrating, that means: all necessary information has to be extracted from the catalogue data themselves. Successful applications of this concept have been made already in the field of aerial photogrammetry.

ARIMA(p,d,q) and Non-Linear Approximation Models for the Fractal Dimension of the Density of Primes Less or Equal to a Positive Integer

2013 ◽  
Vol 1 (2) ◽  
pp. 177-191
Author(s):  
Roberto Padua ◽  
Rodel Azura ◽  
Mark Borres ◽  
Adriano Patac Jr. ◽  
◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Positive Integer ◽  
Linear Approximation ◽  
Non Linear ◽  
Approximation Models
Sign in / Sign up

Export Citation Format

Share Document