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The + and invariants keep track of how curves change under these transformations and deformations. The + invariant increases by 2 when a direct self-tangency move creates new self-intersection points (and decreases by 2 when such points are eliminated), while decreases by 2 when an inverse self-tangency move creates new intersections (and increases by 2 when they are eliminated).
Representation of a lumped model consisting of a voltage source and a resistor. The lumped-element model (also called lumped-parameter model, or lumped-component model) is a simplified representation of a physical system or circuit that assumes all components are concentrated at a single point and their behavior can be described by idealized mathematical models.
In cryptography, higher-order differential cryptanalysis is a generalization of differential cryptanalysis, an attack used against block ciphers.While in standard differential cryptanalysis the difference between only two texts is used, higher-order differential cryptanalysis studies the propagation of a set of differences between a larger set of texts.
Since a single round is usually cryptographically weak, many attacks that fail to work against the full version of ciphers will work on such reduced-round variants. The result of such attack provides valuable information about the strength of the algorithm, [9] a typical break of the full cipher starts out as a success against a reduced-round ...
Slightly less computationally expensive than a birthday attack, [15] but for practical purposes, memory requirements make it more expensive. MD4: 2 64: 3 operations 2007-03-22 Finding collisions almost as fast as verifying them. [16] PANAMA: 2 128: 2 6: 2007-04-04 Paper, [17] improvement of an earlier theoretical attack from 2001. [18] RIPEMD ...
In cryptography, a timing attack is a side-channel attack in which the attacker attempts to compromise a cryptosystem by analyzing the time taken to execute cryptographic algorithms. Every logical operation in a computer takes time to execute, and the time can differ based on the input; with precise measurements of the time for each operation ...
In computer science, a loop variant is a mathematical function defined on the state space of a computer program whose value is monotonically decreased with respect to a (strict) well-founded relation by the iteration of a while loop under some invariant conditions, thereby ensuring its termination.
In the mathematical theory of knots, a finite type invariant, or Vassiliev invariant (so named after Victor Anatolyevich Vassiliev), is a knot invariant that can be extended (in a precise manner to be described) to an invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and does not vanish on some singular knot with 'm' singularities.