• curveOperation.h, curveOperation.c: number operations and curve operations efficiency evaluation, the number to be operated is a random number within 1000, introducing the $Type \ A$ curve in the PBC library to complete the curve operations efficiency evaluation.
• fips202.h, fips202.c: hash operations implementation reference, based on the public domain implementation in crypto_hash/keccakc512/simple/ from Keccakc512Reference by Ronny Van Keer and the public domain "TweetFips202" implementation from Fips202Reference by Gilles Van Assche, Daniel J. Bernstein, and Peter Schwabe.
• matrixOperation.h, matrixOperation.h: evaluate the effciency of matrix/vector addition/multiplication operations with the help of the Eigen library, focusing on the efficiency of atomic operations in the 18' Abdallah et al. scheme and the 21' Qian et al. scheme.
• atomicCompuationComparison.c/atomicComputationComparison.cpp: the main function of the atomic operation evaluation, which can be written to adapt the cpp file to the matrix operations evaluation function to complete the evaluation of the efficiency of matrix operations or the C file to adapt the curve operations evaluation function to complete the evaluation of the efficiency of curve operations.

Complie Options:

• cpp file: g++ -fdiagnostics-color=always -g ${workspaceFolder}/src/atomicComputationComparison/*.cpp -o ${fileDirname}/${fileBasenameNoExtension}.
• C file: gcc -fdiagnostics-color=always -g ${workspaceFolder}/src/atomicComputationComparison/*.c -lgmp -lpbc -I/usr/local/include/pbc -o ${fileDirname}/${fileBasenameNoExtension}, where the include path after the option -I could be replaced by your own include path.

• AES.h, AES.c: the C implementation of performance evaluation of $AES-256$ symmetric algorithm with the help of openssl/aes.h.
• otherAlgorithmsTest.c: the entry function for AES efficiency evaluation function.

Compile Options: gcc -fdiagnostics-color=always -g ${workspaceFolder}/src/otherAlgorithmComparison/*.c -lssl -lcrypto -o ${fileDirname}/${fileBasenameNoExtension}

• cpucycles.h, cpucycles.c: CPU operations utilized in the gaussianSampling files, which achieves sampling acceleration using assembly instructions.
• dataEmbedding.h, dataEmbedding.c: receive the specified binary and convert the original decimal numbers to polynomial coefficients in that binary (including coefficients embedding and extraction), supporting the specified embedding position.
• Dilithium.h, Dilithium.c: the implementation of Dilithium signature with the help of liboqs library, including the key generation, signature generation and verification process.
• fips202.h, fips202.c: hash operations implementation reference.
• Fisher-YatesShuffle.h, Fisher-YatesShuffle.c: the implementation of FYS shuffle for the input array.
• gaussianSampling.h, gaussianSampling.c: discrete Gaussian sampling operations to figure out the coefficients of sampled polynomials, whose coefficients are located in $[4,6)$ .
• numberCRT.h, numberCRT.c: the implementation of Chinese Remainder Theorem for numbers, including the initialization stage, the data process stage and the data recovery stage. TODO: import Miracllibrary to achieve the operations on large number.
• params.h: parameters in FTCR-LMPPDA scheme, including parameters for $PH-NTRU$ , parameters for $Dilithium$ and other general limitiations to ensure proper system operations.
• PH-NTRU.h, PH-NTRU.c: the implementation of $PH-NTRU$ cryptosystem, including the key generation(public key & private key), the encryption process and related decryption process, finally the homomorphic addition operation.
• poly.h, poly.c: the implementation for polynomials defination and operations utilized in $PH-NTRU$ implementation and throughout the whole scheme.
• randombytes.h, randombytes.c: random bytes generation algorithm for specific bytes length.
• zeroSumRandomNumber.h, zeroSumRandomNumber.c: the implementation of the generation and update process of zero-sum random number designed for the collusion resistance of different participants.

Compile Options:

# Makefile for FTCR-LMPPDA program
# The executable file is shown as ./FTCR-LMPPDA1.00 in Linux system
VERSION =1.00
CC =gcc
DEBUG =-DUSE_DEBUG
CFLAGS =-Wall -O

SOURCES =$(wildcard ./*.c)
INCLUDES =-I/usr/include/
LIB_NAMES =-lm -loqs
LIB_PATH =-L/usr/local/lib/


OBJ =$(patsubst %.c, %.o, $(SOURCES))
TARGET =FTCR-LMPPDA

# compile
%.o: %.c
$(CC) $(INCLUDES) $(DEBUG) -c $(CFLAGS) $< -o $@

# links
$(TARGET):$(OBJ)
$(CC) $(OBJ) $(LIB_PATH) $(LIB_NAMES) -o ./$(TARGET)$(VERSION)
@rm -rf $(OBJ)


.PHONY:clean
clean:
@echo "Remove linked and compiled files....."
rm -rf $(OBJ) $(TARGET) ./

The final executable file could be found as FTCR-LMPPDA1.00 in the path /src/.

• testDGS.h, testDGS.c: the tests for discrete Gaussian distribution sampler.
• testDilithium.h, testDilithium.c: the tests and usage of Dilithium signature algorithm.
• testNumberCRT.h, testNumberCRT.c: the tests and usage of Chinese Remainder Theorem for numerical data.
• testPH-NTRU.h, testPH-NTRU.c: the tests and usage of $PH-NTRU$ cryptosystem.
• testZeroSumRandomNumber.h, testZeroSumRandomNumber.c: the tests and usage of the generation, distribution and update of the zero-sum random numbers.

Compile Options:

# Makefile for the test process for all unit, including discrete Gaussian Sampler, Dilithium signature, numberCRT, PH-NTRU encryption, polynomial operations, 
# generation, distribution and update of zero-sum random numbers
VERSION =1.00
CC =gcc
DEBUG =-DUSE_DEBUG
CFLAGS =-Wall -O

SOURCES =$(wildcard ../src/*.c ./*.c)
INCLUDES =-I/usr/include/
LIB_NAMES =-lm -loqs
LIB_PATH =-L/usr/local/lib/


OBJ =$(patsubst %.c, %.o, $(SOURCES))
TARGET =unitTest

# compile
%.o: %.c
	$(CC) $(INCLUDES) $(DEBUG) -c $(CFLAGS) $< -o $@

# links
$(TARGET):$(OBJ)
	$(CC) $(OBJ) $(LIB_PATH) $(LIB_NAMES) -o ./$(TARGET)$(VERSION)
	@rm -rf $(OBJ)


.PHONY:clean
clean:
	@echo "Remove linked and compiled files....."
	rm -rf $(OBJ) $(TARGET) ./

The final executable file could be found as unitTest1.00 in the path /test/.

This folder holds Python and Sage scripts for evaluating the effciency of operations in five types of transformation algorithms (data embedding and extraction, Horner's Rule, numerical Chinese Remainder Theorem, polynomial Chinese Remainder Theorem and super-increasing sequence) utilized between multidimensional data and single dimensional data. The specific analysis results are stored in /Multidimensional-Transformation-Comparison-Python/Multidimensional-Transformation-Comparision-Result.md.

• atomicOperating.py: the efficiency evaluation of atomic operations including addition, multiplication, division, modular and modular inverse with the help of line_profiler library in Python.
• dataInsert.py: the efficiency evaluation of data embedding and extraction operations, including data embedding and data extraction.
• hornerRule.py: the efficiency evaluation of Horner's Rule, including initialization, data process and data recovery stages.
• numberCRT.py: the efficiency evaluation of Chinese Remainder Theorem for numerical data with the help of libnum and gmpy2 library.
• polyCRT.sage: the efficiency evaluation of Chinese Remainder Theorem for polynomial data coded in Sage script.
• superincreasingSequence.py: the efficiency evaluation of super-increasing sequence with the help of libnum library.
• Multidimensional-Transformation-Comparison-Result.md: Markdown file where stores the efficiency evaluation results of five types of transformation methods.

1. Protocol Construction

• To build the FTCR-LMPPDA raw protocol, download the liboqs library and execute the compile option, placing the compiled generated header files under /usr/include/ and the library files under /usr/local/lib.
• Execute make command under /src/, after compile and link operations, the executable file FTCR-LMPPDA1.00 could be found in /src/.

2. Unit Test

To test the operation of each module of the protocol, execute make command in /test/ after completing the installation of liboqs library, after complie and link operations, the executable file unitTest1.00 could be found in /test/.

3. Crosscompiling for Raspberry Pi

To build the FTCR-LMPPDA raw protocol in the Raspberry Pi development board with the pre-installation of Ubuntu20.04 system, first the re-compile of liboqs library with cross-compiling method is needed. Go to the SSH interface and utilize the command lscpu to view the architecture information. After obtaining the architecture information, take aarch64 as an example, download the corresponding gcc compiler on Ubuntu virtual machine: sudo apt-get install gcc-aarch64-linux-gnu. Modify liboqs/.CMake/toolchain_rasppi.cmake as follow, which is utilized to generate the cmake configuration file for cross-compiling the ARM architecture libraries on Linux system.

set(CMAKE_SYSTEM_NAME Linux)
set(CMAKE_SYSTEM_PROCESSOR aarch64)
set(CMAKE_CROSSCOMPILING ON)

set(CMAKE_C_COMPILER aarch64-linux-gnu-gcc)

set(CMAKE_FIND_ROOT_PATH_MODE_PROGRAM NEVER)
set(CMAKE_FIND_ROOT_PATH_MODE_LIBRARY ONLY)
set(CMAKE_FIND_ROOT_PATH_MODE_INCLUDE ONLY)
set(CMAKE_FIND_ROOT_PATH_MODE_PACKAGE ONLY)

add definitions( -DOQS_USE_RASPBERRY_PI)

Modify the CMAKE_SYSTEM_PROCESSOR and CMAKE_C_COMPILER setting options according to the architecture of Raspberry Pi and corresponding C compiler. Then execute the following commands in /build/ directory:

cmake -GNinja -DCMAKE_TOOLCHAIN_FILE=../.CMake/toolchain_rasppi.cmake -DOQS_USE_OPENSSL=OFF -DBUILD_SHARED_LIBS=ON ..
cmake ..
ninja
sudo ninja install

Copy all the dynamic link libraries from the generated /lib/ folder to the Raspberry Pi and execute the following commands:

cd ./lib && sudo cp ./liboqs.* /usr/local/lib
export LD_LIBRARY_PATH=/usr/local/lib/:$LD_LIBRARY_PATH
make

Attention: delete the cpucycles.h and cpucycles.c files in order for the normal operations of our protocol in the Raspberry Pi.

The installation addresses and documatations of all third-party libraries utilized in our project are listed below:

1. line_profiler

• Installation: pip3 install line_profiler;
• Reference: Usage of line_profile;

2. libnum& gmpy2

Installation: pip3 install libnum, pip3 install gmpy2;

3. Sagemath

• Tutorial: Sagemath Tutorial;
• Reference: Official Website of Sagemath;
• Installation: Installation and usage of Sage in Ubuntu20.04;

liboqs: liboqsReference;

OpenSSL: OpenSSL, Official Website of OpenSSL; pqNTRUSign: pqNTRUSign

1. PBC

• Installation: PBC environment configuration in Linux;
• Tutorial: 《基于配对的密码学》;
• Reference: pbc in Github;

2. Eigen

• Installation: The introduction, installation and usage of Eigen
• Reference: Eigen in Github;