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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 340
Author(s):  
Nurul Nur Hanisah Adenan ◽  
Muhammad Rezal Kamel Ariffin ◽  
Siti Hasana Sapar ◽  
Amir Hamzah Abd Ghafar ◽  
Muhammad Asyraf Asbullah
Keyword(s):  
Rsa Cryptosystem ◽  
Small Roots ◽  
Integer Polynomial ◽  
Least Significant Bits

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.

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.

Polynomials for Kloosterman Sums

2007 ◽  
Vol 50 (1) ◽  
pp. 71-84 ◽  
Author(s):  
S. Gurak
Keyword(s):  
Finite Fields ◽  
Complete System ◽  
Kloosterman Sums ◽  
Multiplicative Inverse ◽  
Rational Field ◽  
Image Position ◽  
Explicit Determination

AbstractFix an integer m > 1, and set ζm = exp(2πi/m). Let denote the multiplicative inverse of x modulo m. The Kloosterman sums , satisfy the polynomialwhere the sum and product are taken over a complete system of reduced residues modulo m. Here we give a natural factorization of fm(x), namely,where σ runs through the square classes of the group of reduced residues modulo m. Questions concerning the explicit determination of the factors (or at least their beginning coefficients), their reducibility over the rational field Q and duplication among the factors are studied. The treatment is similar to what has been done for period polynomials for finite fields.

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.

Simple Identification of Electron Diffraction Ring Patterns

1969 ◽  
Vol 27 ◽  
pp. 160-161
Author(s):  
Carolyn Nohr ◽  
Ann Ayres
Keyword(s):  
Electron Microscope ◽  
Electron Diffraction ◽  
Diffraction Ring ◽  
Image Position

Texts on electron diffraction recommend that the camera constant of the electron microscope be determine d by calibration with a standard crystalline specimen, using the equation

Atomic orientation effects in proton stopping at low velocity

1983 ◽  
Vol 41 ◽  
pp. 708-709
Author(s):  
Kin Lam
Keyword(s):  
Polycrystalline Material ◽  
Charged Particles ◽  
Target Material ◽  
Stopping Power ◽  
Low Velocity ◽  
Electronic Density ◽  
Interatomic Distances ◽  
Frame Work ◽  
Image Position ◽  
Atomic Orientation

The energy of moving ions in solid is dependent on the electronic density as well as the atomic structural properties of the target material. These factors contribute to the observable effects in polycrystalline material using the scanning ion microscope. Here we outline a method to investigate the dependence of low velocity proton stopping on interatomic distances and orientations.The interaction of charged particles with atoms in the frame work of the Fermi gas model was proposed by Lindhard. For a system of atoms, the electronic Lindhard stopping power can be generalized to the formwhere the stopping power function is defined as

A Magnetic Spectrometer for a Scanning Transmission Electron Microscope

1974 ◽  
Vol 32 ◽  
pp. 436-437
Author(s):  
A. Kosiara ◽  
J. W. Wiggins ◽  
M. Beer
Keyword(s):  
Scanning Transmission Electron Microscope ◽  
Magnetic Spectrometer ◽  
Fringe Field ◽  
Curvature Radius ◽  
Magnetic Pole ◽  
Quadrupole Field ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Under Construction ◽  
Image Position

A magnetic spectrometer to be attached to the Johns Hopkins S. T. E. M. is under construction. Its main purpose will be to investigate electron interactions with biological molecules in the energy range of 40 KeV to 100 KeV. The spectrometer is of the type described by Kerwin and by Crewe Its magnetic pole boundary is given by the equationwhere R is the electron curvature radius. In our case, R = 15 cm. The electron beam will be deflected by an angle of 90°. The distance between the electron source and the pole boundary will be 30 cm. A linear fringe field will be generated by a quadrupole field arrangement. This is accomplished by a grounded mirror plate and a 45° taper of the magnetic pole.

Optimizing conditions for x-ray microchemical analysis in analytical electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 548-549 ◽  
Author(s):  
N. J. Zaluzec
Keyword(s):  
Solid Angle ◽  
Analytical Electron Microscopy ◽  
Incident Beam ◽  
Thin Foil ◽  
Experimental Conditions ◽  
X Ray ◽  
Microchemical Analysis ◽  
Analytical Electron ◽  
Image Position ◽  
Incident Beam Energy

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation

Sign in / Sign up

Export Citation Format

Share Document