scholarly journals A simple permutation‐based test of intermodal correspondence

2021 ◽  
Author(s):  
Sarah M. Weinstein ◽  
Simon N. Vandekar ◽  
Azeez Adebimpe ◽  
Tinashe M. Tapera ◽  
Timothy Robert‐Fitzgerald ◽  
...  
Keyword(s):  
Simple Permutation

scholarly journals Human-readable Proof of the Related-Key Security of AES-128

2017 ◽  
pp. 59-83 ◽  
Author(s):  
Khoongming Khoo ◽  
Eugene Lee ◽  
Thomas Peyrin ◽  
Siang Meng Sim
Keyword(s):  
Block Cipher ◽  
Internal State ◽  
Meaningful Information ◽  
Key Schedule ◽  
Simple Permutation ◽  
Computer Based ◽  
First Time ◽  
Truncated Differential

The related-key model is now considered an important scenario for block cipher security and many schemes were broken in this model, even AES-192 and AES-256. Recently were introduced efficient computer-based search tools that can produce the best possible related-key truncated differential paths for AES. However, one has to trust the implementation of these tools and they do not provide any meaningful information on how to design a good key schedule, which remains a challenge for the community as of today. We provide in this article the first human-readable proof on the minimal number of active Sboxes in the related-key model for AES-128, without any help from a computer. More precisely, we show that any related-key differential path for AES-128 will respectively contain at least 0, 1, 3 and 9 active Sboxes for 1, 2, 3 and 4 rounds. Our proof is tight, not trivial, and actually exhibits for the first time the interplay between the key state and the internal state of an AES-like block cipher with an AES-like key schedule. As application example, we leverage our proofs to propose a new key schedule, that is not only faster (a simple permutation on the byte positions) but also ensures a higher number of active Sboxes than AES-128’s key schedule. We believe this is an important step towards a good understanding of efficient and secure key schedule designs.

Stochastic scheduling on a repairable machine with Erlang uptime distribution

1998 ◽  
Vol 30 (4) ◽  
pp. 1073-1088 ◽  
Author(s):  
Wei Li ◽  
W. John Braun ◽  
Yiqiang Q. Zhao
Keyword(s):  
Stochastic Scheduling ◽  
Weighted Sum ◽  
Machine Breakdown ◽  
Simple Permutation ◽  
Number Of Tardy Jobs ◽  
Weighted Number ◽  
General Distributions ◽  
Tardy Jobs

A set of jobs is to be processed on a machine which is subject to breakdown and repair. When the processing of a job is interrupted by a machine breakdown, the processing later resumes at the point at which the breakdown occurred. We assume that the machine uptime is Erlang distributed and that processing and repair times follow general distributions. Simple permutation policies on both machine parameters and the processing distributions are given which minimize the weighted number of tardy jobs, weighted flow times and the weighted sum of the job delays.

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