NTRU

Introduction

Just a simple implementation of NTRU which is one of the Round-3 Finalists of Post-Quantum Cryptography in Public-key Encryption and Key-establishment Algorithms. For the same reason, sympy is used for polynomial. So for the larger polynomial rings, this might needs more works. numpy is also needed for many things to run this. This is just for studying purposes so the code can be unoptimized and outputs will be uncompressed. Do not use this for actual cryptographic uses.

Moreover, the post-quantum security parameters are suggested from IEEE p1363.1 Standard [1].

At the moment, there is only NTRUEncrypt (& NTRUDecrypt).

To-do & Work-in-progress

• Working on NTRUSign.
• Resolving this program's poor performance on kem & ss-kem algorithm, so it needs to be reworked in order to handle them.

Installation

• No installation needed, but you need to have sympy and numpy in python.
• After that you can run the program by executing the main.py file .
• Also pypy3 is optional.

Parameters [2]

• High security

  • -S4 : Optimized for size.
  • -C4 : Optimized for cost.
  • -F4 : Optimized for speed.

• Moderate security : -S3, -C3, -F3

• Low security : -S2, -C2, -F2

• Lowest security : -S1, -C1, -F1

• If you don't pick parameter, it will use the default parameter which is F4.

Parameter Set	N	p	q	dg	df	dr
(S1) ees401ep1	401	3	2048	133	113	113
(S2) ees449ep1	449	3	2048	149	134	134
(S3) ees677ep1	677	3	2048	225	157	157
(S4) ees1087ep2	1087	3	2048	362	120	120
(C1) ees541ep1	541	3	2048	180	49	49
(C2) ees613ep1	613	3	2048	204	55	55
(C3) ees887ep1	887	3	2048	295	81	81
(C4) ees1171ep1	1171	3	2048	390	106	106
(F1) ees659ep1	659	3	2048	219	38	38
(F2) ees761ep1	761	3	2048	253	42	42
(F3) ees1087ep1	1087	3	2048	362	63	63
(F4) ees1499ep1	1499	3	2048	499	79	79

Generating Key

• To generate keys. We run the main.py with parameter -g.
• To change file name of the keys. We add parameter -k. (Default is ntru).

Example

• To generate public and private keys with high security, optimized for speed and named "test_key".

python3 main.py -F4 -g -k test_key

• To generate keys with your own parameters.

python3 main.py -g -N 1499 -p 3 -q 2048 -dg 499 -df 79 -dr 79

Encrypting

• To encrypt a string, use -estr, and -efile for a file
• To define the output, you can use -of to write it in a file, and -ot will print the output to the screen.

Example

• To encrypt a string "Hello" with key named "test_key" and print the output on the screen.

python3 main.py -k test_key -estr "Hello" -ot

• To encrypt a file named "Hi.txt" with key named "test_key" and write it in the file named "post_hi.bin"

python3 main.py -k test_key -efile Hi.txt -of post_hi.bin

Decrypting

• Same for encrypting, we have -dstr for a string and -dfile for a file.
• Both -of and -otare also working for decrypting too.

Example

• To decrypt a cyphertext of "Hello" we did earlier with key named "test_key" and print the output on the screen.

python3 main.py -k test_key -dstr "12 -16 18 -4 -15 -28 -23 -20 31 31 -13 7 9 21 -2 4 25 -20 -14 -30 13 3 1 -10 -9 27 -20 -13 5 -31 -13 15 3 -22 13 -2 21 -19 -27 20 -31 25 -14 -3 3 -15 -11 18 -22 -1 -31 -3 -7 21 20 19 -25 -11 25 24 32 -21 -14 -10 19 -15 -26 17 -12 -17 8 -5" -ot

• To decrypt a file named "post_hi.bin" with key named "test_key" and write it in the file named "post_post_hi.bin"

python3 main.py -k test_key -dfile Hi.txt -of post_post_hi.bin

Notes

References

1 : "IEEE Standard Specification for Public Key Cryptographic Techniques Based on Hard Problems over Lattices," in IEEE Std 1363.1-2008 , vol., no., pp.1-81, 10 March 2009, doi: 10.1109/IEEESTD.2009.4800404.

2 : T. Kim and M. -K. Lee, "Efficient and Secure Implementation of NTRUEncrypt Using Signed Sliding Window Method," in IEEE Access, vol. 8, pp. 126591-126605, 2020, doi: 10.1109/ACCESS.2020.3008182.