关于对小指数RSA的赫尔曼-梅格子分析的注释.
Abul Kalam1, Sudeshna Karmakar2, Santanu Sarkar3
1Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, Tamil Nadu, India. abulkalam.sunny@gmail.com.
Scientific reports
|August 5, 2025
概括
研究人员在15年前的一种基于晶格的加密分析方法中发现了小RSA指数的错误. 修正后的边界显著较低,精细的方法实现了波内-达菲边界,并减少了格子尺寸.
科学领域:
- 密码学 密码学 密码学 密码学
- 数学理论 数学理论
- 计算机科学 计算机科学
背景情况:
- 赫尔曼-梅方法 (PKC 2010) 提出了一种基于格子的方法,用于用小指数对RSA进行密码分析.
- 这种方法的目的是通过未拆除的线性化实现d < N^{1} - 1/sqrt{2}) 的理论边界.
研究的目的:
- 为了识别和纠正基于格子的赫尔曼-梅方法的对比分析中的错误.
- 改进赫尔曼-梅格子结构以改善加密分析界限.
- 用小指数重新评估RSA的安全影响.
主要方法:
- 详细分析赫尔曼-梅格子结构的非对称行为.
- 来自基于格子的加密分析的数学界限的修订.
- 修改格子结构以提高效率并实现更严格的界限.
主要成果:
- 确定了赫尔曼-梅方法的原始异面分析中的一个错误,纠正了d < N^0.292256.6的边界.
- 这一修订后的边界严格地低于之前建立的博内-达菲边界.
- 赫尔曼-梅格子结构得到了改进,成功地实现了带有减少格子尺寸的博内-达菲结合.
结论:
- 具有小指数的RSA的安全分析需要考虑更正的,更紧的边界.
- 精细的格子结构为加密分析提供了更有效的方法,与Boneh-Durfee边界相匹配.
- 这项工作纠正了长期存在的错误,并促进了对基于格子的加密分析技术的理解.
相关概念视频
Routh-Hurwitz Criterion II
407
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
407
Norton's Theorem
780
Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the...
780
Bewley Lattice Diagram
859
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
859
Routh-Hurwitz Criterion I
333
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
333
Trends in Lattice Energy: Ion Size and Charge
24.2K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
24.2K
Hückel's Rule Diagram of π MOs: Frost Circle
4.7K
The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so...
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so...
4.7K


