The convergence constants and non linear approximations of fusion frames

2021 ◽  
Vol 12 (3) ◽  
Author(s):  
Yuxiang Xu ◽  
Jinsong Leng
Keyword(s):  
Fusion Frames ◽  
Linear Approximations ◽  
Non Linear

Quantum splines for non-linear approximations

2020 ◽  
Author(s):  
Antonio Macaluso ◽  
Luca Clissa ◽  
Stefano Lodi ◽  
Claudio Sartori
Keyword(s):  
Linear Approximations ◽  
Non Linear

scholarly journals Quantum Algorithm to Construct Linear Approximation of an S-Box

2019 ◽  
Vol 8 (4) ◽  
pp. 9096-9099
Keyword(s):  
Linear Approximation ◽  
Time Complexity ◽  
Block Cipher ◽  
Quantum Algorithm ◽  
Correctness Proof ◽  
Linear Approximations ◽  
Input Size ◽  
Non Linear ◽  
Classical Computing ◽  
Symmetric Block

Linear cryptanalysis, a Known-Plaintext Attack, for symmetric block cipher works by constructing linear approximations of the non-linear components of the cipher. The only component which introduces non-linearity in the symmetric block cipher is an S-box. Using classical computing algorithms, the best known solution to find a linear approximation of a non-linear function, in this case an S-box, requires 𝑶(𝟐 𝒏 ) queries to the S-box and 𝑶(𝟐 𝟐𝒏+𝒎) time-complexity, where 𝒏 is the input size of the S-box and 𝒎 is the output size. In this paper, a quantum algorithm is presented which can produce best linear approximations of a non-linear S-box using only 𝑶(𝟐 𝒎) queries to S-box with 𝑶(𝒏𝟐 𝒎) time-complexity. The proposed algorithm shows a significant improvement over the classical algorithm. Correctness proof of the proposed quantum algorithm is presented along with an example.

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