1. Introduction

This repository contains auxiliary material taken from the dCTIDH repository. In particular, we list the modifications performed on the code below.

Modified files:
- dCTIDH/CMakeLists.txt: added flag option for using radical 3-isogenies.
- dCTIDH/main/CMakeLists.txt: added flag option for using radical 3-isogenies.
- dCTIDH/main/ctidh.c: added benchmark for the key generation (keygen).
- dCTIDH/src/CMakeLists.txt: added flag option for using radical 3-isogenies.
- dCTIDH/src/CMakeLists.txt: added isogeny_walks_3fp to compilation (line 197).
- dCTIDH/src/CTIDH/ctidh.c: removed used of (at most) the fifth smallest isogeny degrees (3,5,7,11,13).
- dCTIDH/src/CTIDH/ctidh.c: Added radical 3-isogeny's call (line 387-389).
- dCTIDH/src/CTIDH/ctidh.h: added radical 3-isogeny data in the private key
- dCTIDH/src/CTIDH/isogeny_walks.h: added radical 3-isogeny header
- dCTIDH/src/CTIDH/isogeny_walks_3_fp.c: added radical 3-isogeny source code
- dCTIDH/src/common/primes.h: updated exponent of two.
- dCTIDH/src/common/primes2047m1l226.c: removed used of (at most) the fifth smallest isogeny degrees (3,5,7,11,13).
- dCTIDH/src/common/primes2047m4l205.c: removed used of (at most) the fifth smallest isogeny degrees (3,5,7,11,13).
- dCTIDH/src/common/primes2047m6l194.c: removed used of (at most) the fifth smallest isogeny degrees (3,5,7,11,13).
- dCTIDH/src/common/skgen.c: added radical 3-isogeny.
- dCTIDH/src/common/validate.c: updated according to remove (at most) the fifth smallest isogeny degrees (3,5,7,11,13)..
New files:
- dCTIDH/src/CTIDH/isogeny_walks_3_fp.c: added radical 3-isogeny layer.
- dCTIDH/src/CTIDH/isogeny_walks.h: added namespace for the radical 3-isogeny layer.

In addition, this repository includes the corresponding implementation of projective radical 3-isogenies.

2. Building

Use the flag option -DOPT_RAD=ARG_RAD with ARG_RAD=[0/1/2/3/4/5] to employ radical 3-isogenies. The code takes ARG_RAD=0 by default.

# Only necessary first time (generally)
rm -rf build/
mkdir build && cd build
cmake .. -DOPT_RAD=5
 
# Building
make

This builds the executables for 3 versions:

2047m1l226
2047m4l205
2047m6l194

3. Benchmarking

usage (when in /build/main) :   
    ./ctidh-2047m1l226.main             // for a quick test
    ./ctidh-2047m1l226.main -bact [number of runs]  // run benchmark for the action
    ./ctidh-2047m1l226.main -bkey [number of runs]  // run benchmark for the action

The benchmarks can be analyzed using the analyze_bench.py script:

$ ./build/main/ctidh-2047m1l226.main -bkey 500 > bench_keygen.out

$ python3 analyze_bench.py < bench_action.out

4. Benchmarking Script

To run the benchmarking script and generate the related statistics, please run

ssec-23/dCTIDH$ mkdir statistics_output

ssec-23/dCTIDH$ sudo bash benchmark_opt_rad.sh

This will generate a tree structure like the one shown below

To run the statistics, for a particular OPT_RAD, execute

ssec-23/dCTIDH$ python3 analyze_bench.py < statistics_output/<RESULTS_FOLDER>/OPT_RAD_<SELECTED_OPT_RAD>/bench_<KEYGEN_OR_ACT>_<dCTIDH_PRIME>_opt_rad_<SELECTED_OPT_RAD>.out

Examples:

ssec-23/dCTIDH$ python3 analyze_bench.py < statistics_output/results/OPT_RAD_0/bench_keygen_226_opt_rad_0.out

ssec-23/dCTIDH$ python3 analyze_bench.py < statistics_output/results/OPT_RAD_1/bench_act_205_opt_rad_1.out

This will output the results like the following

where the highlighted number is the desired statistical result.

5. Constant-time Check

If DENABLE_CT_TESTING=ON, checkct versions of the executable are created for all versions, which can be validated with valgrind.

For example, to validate that ctidh-2047m6l194 is constant-time:

valgrind ./main/checkct-2047m6l194.main

6. Licenses