## Average case reductions for Subset Sum and Decoding of Linear Codes (1999)

### BibTeX

@MISC{Arboit99averagecase,

author = {Genevieve Arboit},

title = {Average case reductions for Subset Sum and Decoding of Linear Codes},

year = {1999}

}

### OpenURL

### Abstract

Average case reductions for Subset Sum and Decoding of Linear Codes Genevi`eve Arboit Master of Science Graduate Department of Computer Science University of Toronto 1999 In a 1996 paper, R. Impagliazzo and M. Naor show two average case reductions for the Subset Sum problem (SS). We use similar ideas to obtain stronger and additional such reductions for SS. Furthermore, we use modifications of these ideas to obtain similar reductions for the Decoding of Linear Codes problem (DLC). The theorems give further evidence that the hardest case for Average case SS is when the number of integers is equal to their length. For Average case DLC, the theorems give evidence that the hardest case is when the dimension of the code is equal to the channel capacity times the length of the words. Average case SS and DLC hardness assumptions can be used to obtain one-way functions, pseudorandom generators, and secure private-key cryptography. ii Acknowledgments I dedicate this work to my parents, who ha...