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README.md

kmp-mpc

Oblivious substring search using Obliv-C, sqrtOram and Knuth-Morris-Pratt.

Introduction

One party wants to be able to determine whether its substring is in another party's text. However, both parties want to keep their input private. This multi-party computation (MPC) problem, known as oblivious substring search, can be found across several different fields. In bioinformatics, for example, people might want to allow a company to search their DNA for a particular proprietary pattern, while maintaining privacy.

kmp-mpc uses Obliv-C as a MPC framework. It creates a new variation of the substring search algorithm Knuth-Morris-Pratt to accomodate for Obliv-C's restrictions on oblivious conditional statements and indexing into arrays. To keep memory access patterns hidden, all oblivious indexing into arrays use ORAM. Rather than use the naive solution of reading at each index to hide memory access patterns, this implementation uses sqrtOram reducing the time complexity of oblivious lookups from linear to square-root order.

Test Results

Tests were conducted on two AWS c4.2xlarge nodes. The tests found a linear relationship between text size and run time and a square-root relationship between pattern size and run time.

pattern length text length yao gate count time (s)
1 8192 26463069 11.218935
2 8192 49098407 17.547319
4 8192 93141927 29.464218
8 8192 103474839 35.518375
16 8192 169806418 54.114391
32 8192 281146357 86.611352
64 8192 474221756 142.644258

screen shot 2018-06-22 at 10 09 39 pm

text length yao gate count time (s)
8 153501 0.363900
16 221533 0.371387
32 369885 0.422282
64 715741 0.509723
128 1442328 0.739889
256 2895694 1.217106
512 5803194 2.093564
1024 11621266 3.894311
2048 23269698 7.820184
4096 46615714 14.810030
8192 93141927 29.353847
16384 186194545 59.187216
32768 372300549 120.202773
65536 744515629 231.481555

screen shot 2018-06-22 at 10 09 24 pm

Installation

git clone https://github.com/jnayak1/kmp-mpc.git

export OBLIVC_PATH=/path/to/obliv-c

export SQR_ORAM_PATH=/path/to//sqrtOram

Running

MAX_PATTERN_LENGTH=4 MAX_TEXT_LENGTH=256 make

./a.out [port] -- text.txt & -- server

./a.out [port] [host] pattern.txt -- client

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Knuth Morris Pratt Multi-Party Computation

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