Partial Linearization Method for Network Equilibrium Problems with Elastic Demands

2016 ◽  
pp. 418-429
Author(s):  
Igor Konnov ◽  
Olga Pinyagina
Keyword(s):  
Equilibrium Problems ◽  
Linearization Method ◽  
Network Equilibrium ◽  
Partial Linearization ◽  
Elastic Demands ◽  
Partial Linearization Method ◽  
Network Equilibrium Problems

A Nonlinear Equation Framework for Solving Network Equilibrium Problems

1984 ◽  
Vol 16 (1) ◽  
pp. 67-80 ◽  
Author(s):  
C Fisk
Keyword(s):  
Existence And Uniqueness ◽  
Equilibrium Problems ◽  
Iterative Solution ◽  
System Of Nonlinear Equations ◽  
Network Equilibrium ◽  
Convergence Properties ◽  
Equilibrium Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Network Equilibrium Problems

The author presents a general framework for formulating network equilibrium problems in which the equilibrium conditions are given by a system of nonlinear equations. Existence and uniqueness results are presented, and iterative solution techniques with well-defined convergence properties are suggested. For illustrative purposes, these techniques are applied to a specific two-mode equilibrium model; a discussion comparing some aspects of this approach with other existing approaches is included.

scholarly journals Improved Preimage Attacks on 4-Round Keccak-224/256

2021 ◽  
pp. 217-238
Author(s):  
Le He ◽  
Xiaoen Lin ◽  
Hongbo Yu
Keyword(s):  
Theoretical Analysis ◽  
Degrees Of Freedom ◽  
Linear Structure ◽  
Linearization Method ◽  
Partial Linearization ◽  
Practical Complexity ◽  
Partial Linearization Method ◽  
Preimage Attack

This paper provides an improved preimage attack method on standard 4-round Keccak-224/256. The method is based on the work pioneered by Li and Sun, who design a linear structure of 2-round Keccak-224/256 with 194 degrees of freedom left. By partially linearizing 17 output bits through the last 2 rounds, they finally reach a complexity of 2207/2239 for searching a 4-round preimage. Yet under their strategy, those 17 bits are regarded as independent bits and the linearization costs a great amount of freedom. Inspired by their thoughts, we improve the partial linearization method where multiple output bits can reuse some common degrees of freedom. As a result, the complexity of preimage attack on 4-round Keccak-224/256 can be decreased to 2192/2218, which are both the best known theoretical preimage cryptanalysis so far. To support the theoretical analysis, we apply our strategy to a 64-bit partial preimage attack within practical complexity. It is remarkable that this partial linearization method can be directly applied if a better linear structure with more freedom left is proposed.

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