This class implements the Paillier cryptosystem. More...

#include <Paillier.hpp>

Public Member Functions
	Paillier ()
	Construct a new Paillier object.

	~Paillier ()
	Destroy the Paillier object.

uint64_t	random64 (uint64_t min, uint64_t max)
	Generate a random 64-bit unsigned integer.

uint64_t	fastMod_64t (uint64_t x, uint64_t e, uint64_t n)
	Calculate the modular exponentiation of a base raised to a power modulo a modulus.

uint64_t	gcd_64t (uint64_t a, uint64_t b)
	Calculate the greatest common divisor (GCD) of two 64-bit unsigned integers.

std::vector< uint64_t >	calc_set_same_remainder_divide_euclide_64t (uint64_t n)
	Calculate the set of elements in (Z/n²Z)*.

std::vector< uint64_t >	calc_set_same_remainder_divide_euclide_64t_v2 (uint64_t n, const uint64_t &lambda)
	Calculate the set of elements in (Z/n²Z)* that satisfy the condition L(x) = (x-1)/n where x is a positive integer and mu exists.

uint64_t	choose_g_in_vec_64t (std::vector< uint64_t > &set, const uint64_t &n, const uint64_t &lambda)
	Choose g from the set of elements in (Z/n²Z)* that satisfy the condition L(x) = (x-1)/n where x is a positive integer and mu exists.

uint64_t	choose_g_in_vec_64t_v2 (std::vector< uint64_t > &set)
	Choose g from the set of elements in (Z/n²Z)*.

uint64_t	L_64t (uint64_t x, uint64_t n)
	Calculate L(x).

uint64_t	lcm_64t (uint64_t a, uint64_t b)
	Calculate the least common multiple (LCM) of two 64-bit unsigned integers.

uint64_t	modInverse_64t (uint64_t a, uint64_t n)
	Calculate the modular inverse of a 64-bit unsigned integer modulo a modulus.

uint64_t	pow_uint64_t (uint64_t x, uint64_t n)
	Calculate the power of a 64-bit unsigned integer.

uint64_t	randomZNStar (uint64_t n)
	Choose a random element from the set Z/nZ*.

std::vector< uint64_t >	get_set_ZNZStar (uint64_t n)
	Return the set Z/nZ* as a vector.

std::vector< uint64_t >	get_set_ZN2ZStar (uint64_t n, uint64_t lambda)
	Return the set Z/n²Z* that satisfy the condition gcd(L(g^lambda mod n²), n) = 1 as a vector.

uint64_t	generate_g_64t (uint64_t n, uint64_t lambda)
	Generate g for Paillier cryptosystem.

void	generateMu_64t (uint64_t &mu, const uint64_t &g, const uint64_t &lambda, const uint64_t &n)
	Generate Mu for Paillier cryptosystem.

void	generatePrivateKey_64t (uint64_t &lambda, uint64_t &mu, const uint64_t &p, const uint64_t &q, const uint64_t &n, const uint64_t &g)
	Generate private key for Paillier cryptosystem.

T_out	paillierEncryption (uint64_t n, uint64_t g, T_in m)
	Encrypt a message using Paillier cryptosystem.

T_out	paillierEncryption (uint64_t n, uint64_t g, T_in m, uint64_t r)
	Encrypt a message using Paillier cryptosystem with a given random value.

T_in	paillierDecryption (uint64_t n, uint64_t lambda, uint64_t mu, T_out c)
	Decrypt a ciphertext using Paillier cryptosystem.

Detailed Description

template<typename T_in, typename T_out>
class Paillier< T_in, T_out >

This class implements the Paillier cryptosystem.

Template Parameters

T_in	The input data type.
T_out	The output data type.

Author: Katia Auxilien

Date: April 2024 - May 2024

Constructor & Destructor Documentation

◆ Paillier()

template<typename T_in , typename T_out >

Paillier< T_in, T_out >::Paillier ( )

inline

Construct a new Paillier object.

Author: Katia Auxilien

Date: April 2024 - May 2024

◆ ~Paillier()

template<typename T_in , typename T_out >

Paillier< T_in, T_out >::~Paillier ( )

inline

Destroy the Paillier object.

Author: Katia Auxilien

Date: April 2024 - May 2024

Member Function Documentation

◆ calc_set_same_remainder_divide_euclide_64t()

template<typename T_in , typename T_out >

std::vector< uint64_t > Paillier< T_in, T_out >::calc_set_same_remainder_divide_euclide_64t ( uint64_t n )

inline

Calculate the set of elements in (Z/n²Z)*.

Deprecated: This function is not sufficient for Paillier cryptosystem.

This function calculates the set of elements in (Z/n²Z)* that are coprime to n.

Parameters

uint64_t n - The n parameter of public key.

Returns: std::vector<uint64_t> - The set of elements in (Z/n²Z)* that are coprime to n.

Authors: Katia Auxilien

Date: 30 April 2024 15:51:00

◆ calc_set_same_remainder_divide_euclide_64t_v2()

template<typename T_in , typename T_out >

std::vector< uint64_t > Paillier< T_in, T_out >::calc_set_same_remainder_divide_euclide_64t_v2	(	uint64_t	n,
		const uint64_t &	lambda )

inline

Calculate the set of elements in (Z/n²Z)* that satisfy the condition L(x) = (x-1)/n where x is a positive integer and mu exists.

Deprecated: This function is not sufficient for Paillier cryptosystem.

This function calculates the set of elements in (Z/n²Z)* that satisfy the condition L(x) = (x-1)/n where x is a positive integer and mu exists.

Parameters

uint64_t	n - The n parameter of public key.
const	uint64_t &lambda - The lambda parameter of private key.

Returns: std::vector<uint64_t> - The set of elements in (Z/n²Z)* that satisfy the condition L(x) = (x-1)/n where x is a positive integer and mu exists.

Authors: Katia Auxilien

Date: 22 May 2024 14:45:00

◆ choose_g_in_vec_64t()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::choose_g_in_vec_64t	(	std::vector< uint64_t > &	set,
		const uint64_t &	n,
		const uint64_t &	lambda )

inline

Choose g from the set of elements in (Z/n²Z)* that satisfy the condition L(x) = (x-1)/n where x is a positive integer and mu exists.

Deprecated: This function is not sufficient for Paillier cryptosystem.

This function chooses g from the set of elements in (Z/n²Z)* that satisfy the condition L(x) = (x-1)/n where x is a positive integer and mu exists.

Parameters

std::vector<uint64_t>	&set - The set of elements in (Z/n²Z)* that satisfy the condition L(x) = (x-1)/n where x is a positive integer and mu exists.
const	uint64_t &n - The n parameter of public key.
const	uint64_t &lambda - The lambda parameter of private key.

Returns: uint64_t - The chosen value of g.

Authors: Katia Auxilien

Date: 02 May 2024

◆ choose_g_in_vec_64t_v2()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::choose_g_in_vec_64t_v2 ( std::vector< uint64_t > & set )

inline

Choose g from the set of elements in (Z/n²Z)*.

Deprecated: This function is not sufficient for Paillier cryptosystem.

This function chooses g from the set of elements in (Z/n²Z)*.

Parameters

std::vector<uint64_t> &set - The set of elements in (Z/n²Z)*.

Returns: uint64_t - The chosen value of g.

Authors: Katia Auxilien

Date: 22 May 2024 14:45:00

◆ fastMod_64t()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::fastMod_64t	(	uint64_t	x,
		uint64_t	e,
		uint64_t	n )

inline

Calculate the modular exponentiation of a base raised to a power modulo a modulus.

This function calculates the modular exponentiation of a base raised to a power modulo a modulus using the square-and-multiply algorithm.

Parameters

uint64_t	x - The base value.
uint64_t	e - The exponent value.
uint64_t	n - The n parameter of public key.

Returns: uint64_t - The result of the modular exponentiation.

Author: Bianca Jansen Van Rensburg

Date: 30 April 2024

◆ gcd_64t()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::gcd_64t	(	uint64_t	a,
		uint64_t	b )

inline

Calculate the greatest common divisor (GCD) of two 64-bit unsigned integers.

This function calculates the greatest common divisor (GCD) of two 64-bit unsigned integers using the Euclidean algorithm.

Parameters

uint64_t	a - The first integer.
uint64_t	b - The second integer.

Returns: uint64_t - The greatest common divisor of a and b.

Authors: Bianca Jansen Van Rensburg

Date: 30 April 2024

◆ generate_g_64t()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::generate_g_64t	(	uint64_t	n,
		uint64_t	lambda )

inline

Generate g for Paillier cryptosystem.

This function generates g for Paillier cryptosystem such that gcd(L(g^lambda mod n²), n) = 1 where L(u) = (u-1)/n. From program Paillier.java (https://perso.liris.cnrs.fr/omar.hasan/pprs/paillierdemo/) developped by Omar Hasan.

Parameters

uint64_t	n - The n parameter of public key.
uint64_t	lambda - The lambda parameter of private key.

Returns: uint64_t - The generated value of g.

Authors: Katia Auxilien

Date: 23 May 2024 15:00:00

◆ generateMu_64t()

template<typename T_in , typename T_out >

void Paillier< T_in, T_out >::generateMu_64t	(	uint64_t &	mu,
		const uint64_t &	g,
		const uint64_t &	lambda,
		const uint64_t &	n )

inline

Generate Mu for Paillier cryptosystem.

This function generates Mu for Paillier cryptosystem which is used in the decryption process.

Parameters

uint64_t	&mu - The generated value of Mu.
const	uint64_t &g - The generator value.
const	uint64_t &lambda - The Carmichael function of n.
const	uint64_t &n - The modulus value.

Author: Bianca Jansen Van Rensburg

Date: ?

◆ generatePrivateKey_64t()

template<typename T_in , typename T_out >

void Paillier< T_in, T_out >::generatePrivateKey_64t	(	uint64_t &	lambda,
		uint64_t &	mu,
		const uint64_t &	p,
		const uint64_t &	q,
		const uint64_t &	n,
		const uint64_t &	g )

inline

Generate private key for Paillier cryptosystem.

This function generates the private key for Paillier cryptosystem which consists of lambda and Mu values.

Parameters

uint64_t	&lambda - The generated value of lambda.
uint64_t	&mu - The generated value of Mu.
const	uint64_t &p - The first prime factor of n.
const	uint64_t &q - The second prime factor of n.
const	uint64_t &n - The n parameter of public key.
const	uint64_t &g - The generator value.

Author: Bianca Jansen Van Rensburg

◆ get_set_ZN2ZStar()

template<typename T_in , typename T_out >

std::vector< uint64_t > Paillier< T_in, T_out >::get_set_ZN2ZStar	(	uint64_t	n,
		uint64_t	lambda )

inline

Return the set Z/n²Z* that satisfy the condition gcd(L(g^lambda mod n²), n) = 1 as a vector.

This function returns the set Z/n²Z* that satisfy the condition gcd(L(g^lambda mod n²), n) = 1 as a vector.

Parameters

uint64_t	n - The n parameter of public key.
uint64_t	lambda - The lambda parameter of private key.

Returns: std::vector<uint64_t> - The set Z/n²Z* that satisfy the condition gcd(L(g^lambda mod n²), n) = 1 as a vector.

Author: Katia Auxilien

Date: 27 May 2024 15:00:00

◆ get_set_ZNZStar()

template<typename T_in , typename T_out >

std::vector< uint64_t > Paillier< T_in, T_out >::get_set_ZNZStar ( uint64_t n )

inline

Return the set Z/nZ* as a vector.

This function returns the set Z/nZ* as a vector.

Parameters

uint64_t n - The n parameter of public key.

Returns: std::vector<uint64_t> - The set Z/nZ* as a vector.

Author: Katia Auxilien

Date: 23 May 2024 9:18:00

◆ L_64t()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::L_64t	(	uint64_t	x,
		uint64_t	n )

inline

Calculate L(x).

This function calculates L(x) which is used in the generation of Mu and the decryption by Paillier.

Parameters

uint64_t	x - The value of x.
uint64_t	n - The n parameter of public key.

Returns: uint64_t - The value of L(x).

Author: Bianca Jansen Van Rensburg

◆ lcm_64t()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::lcm_64t	(	uint64_t	a,
		uint64_t	b )

inline

Calculate the least common multiple (LCM) of two 64-bit unsigned integers.

This function calculates the least common multiple (LCM) of two 64-bit unsigned integers using the GCD function.

Parameters

uint64_t	a - The first integer.
uint64_t	b - The second integer.

Returns: uint64_t - The least common multiple of a and b.

Author: Bianca Jansen Van Rensburg

◆ modInverse_64t()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::modInverse_64t	(	uint64_t	a,
		uint64_t	n )

inline

Calculate the modular inverse of a 64-bit unsigned integer modulo a modulus.

This function calculates the modular inverse of a 64-bit unsigned integer modulo a modulus using the extended Euclidean algorithm.

Parameters

uint64_t	a - The integer to calculate the modular inverse of.
uint64_t	n - The n parameter of public key.

Returns: uint64_t - The modular inverse of a modulo n.

Author: Bianca Jansen Van Rensburg

◆ paillierDecryption()

template<typename T_in , typename T_out >

T_in Paillier< T_in, T_out >::paillierDecryption	(	uint64_t	n,
		uint64_t	lambda,
		uint64_t	mu,
		T_out	c )

inline

Decrypt a ciphertext using Paillier cryptosystem.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

This function decrypts a ciphertext using Paillier cryptosystem.

Parameters

uint64_t	n - The modulus value.
uint64_t	lambda - The Carmichael function of n.
uint64_t	mu - The Mu value.
T_out	c - The ciphertext to be decrypted.

Returns: T_in - The decrypted message.

Authors: Bianca Jansen Van Rensburg, Katia Auxilien

Date: 13 May 2024

◆ paillierEncryption() [1/2]

template<typename T_in , typename T_out >

T_out Paillier< T_in, T_out >::paillierEncryption	(	uint64_t	n,
		uint64_t	g,
		T_in	m )

inline

Encrypt a message using Paillier cryptosystem.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

This function encrypts a message using Paillier cryptosystem.

Parameters

uint64_t	n - The modulus value.
uint64_t	g - The generator value.
T_in	m - The message to be encrypted.

Returns: T_out - The encrypted message.

Authors: Bianca Jansen Van Rensburg, Katia Auxilien

Date: 13 May 2024

◆ paillierEncryption() [2/2]

template<typename T_in , typename T_out >

T_out Paillier< T_in, T_out >::paillierEncryption	(	uint64_t	n,
		uint64_t	g,
		T_in	m,
		uint64_t	r )

inline

Encrypt a message using Paillier cryptosystem with a given random value.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

This function encrypts a message using Paillier cryptosystem with a given random value.

Parameters

uint64_t	n - The modulus value.
uint64_t	g - The generator value.
T_in	m - The message to be encrypted.
uint64_t	r - The random value.

Returns: T_out - The encrypted message.

Authors: Bianca Jansen Van Rensburg, Katia Auxilien

Date: 13 May 2024

◆ pow_uint64_t()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::pow_uint64_t	(	uint64_t	x,
		uint64_t	n )

inline

Calculate the power of a 64-bit unsigned integer.

This function calculates the power of a 64-bit unsigned integer using recursion.

Parameters

uint64_t	x - The base value.
uint64_t	n - The exponent value.

Returns: uint64_t - The result of the power calculation.

Author: Katia Auxilien

Date: 30 April 2024

◆ random64()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::random64	(	uint64_t	min,
		uint64_t	max )

inline

Generate a random 64-bit unsigned integer.

This function generates a random 64-bit unsigned integer between a given range using the Mersenne Twister algorithm.

Parameters

uint64_t	min - The minimum value of the range.
uint64_t	max - The maximum value of the range.

Returns: uint64_t - A random 64-bit unsigned integer between min and max.

Author: Katia Auxilien

Date: 23 May 2024

◆ randomZNStar()

template<typename T_in , typename T_out >

uint64_t Paillier< T_in, T_out >::randomZNStar ( uint64_t n )

inline

Choose a random element from the set Z/nZ*.

This function chooses a random element from the set Z/nZ*. From program Paillier.java (https://perso.liris.cnrs.fr/omar.hasan/pprs/paillierdemo/) developped by Omar Hasan.

Parameters

uint64_t n - The n parameter of public key.

Returns: uint64_t - The chosen random element from the set Z/nZ*.

Parameters

author Katia Auxilien

Date: 23 May 2024 15:00:00

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Paillier()

◆ ~Paillier()

Member Function Documentation

◆ calc_set_same_remainder_divide_euclide_64t()

◆ calc_set_same_remainder_divide_euclide_64t_v2()

◆ choose_g_in_vec_64t()

◆ choose_g_in_vec_64t_v2()

◆ fastMod_64t()

◆ gcd_64t()

◆ generate_g_64t()

◆ generateMu_64t()

◆ generatePrivateKey_64t()

◆ get_set_ZN2ZStar()

◆ get_set_ZNZStar()

◆ L_64t()

◆ lcm_64t()

◆ modInverse_64t()

◆ paillierDecryption()

◆ paillierEncryption() [1/2]

◆ paillierEncryption() [2/2]

◆ pow_uint64_t()

◆ random64()

◆ randomZNStar()