Implementation of the public-key Paillier Cryptosystem. More...

#include <paillier.h>

Inheritance diagram for SeComLib::Core::Paillier:

Public Member Functions
	Paillier ()
	Default constructor. More...

	Paillier (const PaillierPublicKey &publicKey)
	Creates an instance of the class for homomorphic operations and ecryption. More...

	Paillier (const PaillierPublicKey &publicKey, const PaillierPrivateKey &privateKey)
	Creates an instance of the class for homomorphic operations, ecryption and decryption. More...

	~Paillier ()
	Destructor.

virtual bool	GenerateKeys ()

virtual BigInteger	DecryptInteger (const Ciphertext &ciphertext) const
	Decrypt number. More...

virtual Ciphertext	EncryptIntegerNonrandom (const BigInteger &plaintext) const
	Encrypt number without randomization. More...

virtual Randomizer	GetRandomizer () const
	Compute the random factor required for the encryption operation. More...

virtual Ciphertext	RandomizeCiphertext (const Ciphertext &ciphertext) const
	Randomize encrypted number with a self-generated random value. More...

virtual const BigInteger &	GetMessageSpaceUpperBound () const
	Returns the message space upper bound. More...

virtual size_t	GetMessageSpaceSize () const
	Returns the message space bit size. More...

Public Member Functions inherited from SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >
	CryptoProvider (const unsigned int keyLength)
	Constructor. More...

	CryptoProvider (const PaillierPublicKey &publicKey, const unsigned int keyLength)
	Constructor. More...

	CryptoProvider (const PaillierPublicKey &publicKey, const PaillierPrivateKey &privateKey, const unsigned int keyLength)
	Constructor. More...

virtual	~CryptoProvider ()
	Destructor.

virtual PaillierCiphertext	EncryptInteger (const BigInteger &plaintext) const
	Encrypt an integer and apply randomization. More...

const BigInteger &	GetEncryptionModulus () const
	Returns the modulus required for reducing the encryption after randomization. More...

virtual const BigInteger &	GetPositiveNegativeBoundary () const
	Returns the biggest positive number that can be encrypted without overflowing. More...

const PaillierPublicKey &	GetPublicKey () const
	Public key getter. More...

const PaillierPrivateKey &	GetPrivateKey () const
	Private key getter. More...

Ciphertext	GetEncryptedZero (const bool randomized=true) const
	Returns [0]. More...

Ciphertext	GetEncryptedOne (const bool randomized=true) const
	Returns [1]. More...

Private Member Functions
BigInteger	L (const BigInteger &input, const BigInteger &d) const
	L function evaluator. More...

virtual void	validateParameters ()
	Do nothing for now.

virtual void	doPrecomputations ()
	Precompute values for speedups. More...

	Paillier (const Paillier &)
	Copy constructor - not implemented.

Paillier	operator= (const Paillier &)
	Copy assignment operator - not implemented.

Private Attributes
BigInteger	pMinusOne
	\( p - 1 \)

BigInteger	qMinusOne
	\( q - 1 \)

BigInteger	nMinusOne
	Contains \( n - 1 \).

BigInteger	pSquared
	\( p^2 \)

BigInteger	qSquared
	\( q^2 \)

BigInteger	nSquared
	Contains \( n^2 \).

BigInteger	pTimesPInvModQ
	\( p (p^{-1} \pmod q) \)

BigInteger	qTimesQInvModP
	\( q (q^{-1} \pmod p) \)

BigInteger	hp
	\( L_p(g^{p - 1} (\pmod p^2))^{-1} \pmod p \)

BigInteger	hq
	\( L_q(g^{q - 1} (\pmod q^2))^{-1} \pmod q \)

Additional Inherited Members
Public Types inherited from SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >
typedef PaillierCiphertext	Ciphertext
	Provide public access to the T_Ciphertext type.

typedef PaillierRandomizer	Randomizer
	Provide public access to the T_Randomizer type.

Protected Types inherited from SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >
typedef RandomizerCache < RandomizerContainer < CryptoProvider < PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer > , RandomizerCacheParameters > >	RandomizerCacheType
	Data type of the randomizer cache.

Protected Attributes inherited from SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >
std::unique_ptr < RandomizerCacheType >	randomizerCache
	Lazy loading randomizer cache.

PaillierPublicKey	publicKey
	Public key container.

PaillierPrivateKey	privateKey
	Private key container.

unsigned int	keyLength
	The key length in bits.

std::shared_ptr< BigInteger >	encryptionModulus
	The encryption modulus.

BigInteger	positiveNegativeBoundary
	Contains the delimiter between positive and negative values in the message space (usually \( \lfloor messagespace / 2 \rfloor \))

bool	hasPrivateKey
	Boolean flag that enables decryption if the private key is present.

bool	precomputeSpeedupValues
	Boolean flag that indicates wether doPrecomputations() should precompute certain values.

PaillierCiphertext	encryptedZero
	Contains [0] used as initializer for homomorphic addition accumulators. Precompute it for optimization purposes.

PaillierCiphertext	encryptedOne
	Contains [1].

Detailed Description

Implementation of the public-key Paillier Cryptosystem.

Definition at line 103 of file paillier.h.

Constructor & Destructor Documentation

SeComLib::Core::Paillier::Paillier ( )

Default constructor.

Sets the specified key size from the configuration file (defaults to 1024)

Definition at line 73 of file paillier.cpp.

SeComLib::Core::Paillier::Paillier ( const PaillierPublicKey & publicKey )

Creates an instance of the class for homomorphic operations and ecryption.

Performs required precomputations.

Parameters

publicKey a PaillierPublicKey structure

Definition at line 81 of file paillier.cpp.

SeComLib::Core::Paillier::Paillier	(	const PaillierPublicKey &	publicKey,
		const PaillierPrivateKey &	privateKey
	)

Creates an instance of the class for homomorphic operations, ecryption and decryption.

Performs required precomputations.

Parameters

publicKey	a PaillierPublicKey structure
privateKey	a PaillierPrivateKey structure

Definition at line 92 of file paillier.cpp.

Member Function Documentation

BigInteger SeComLib::Core::Paillier::DecryptInteger ( const Ciphertext & ciphertext ) const

virtual

Decrypt number.

If \( plaintext \geq \lfloor messagespace / 2 \), it is remapped to a negative value.

Parameters

ciphertext the ciphertext integer

Returns: Deciphered plaintext

Exceptions

std::runtime_error operation requires the private key

Apply CRT for decryption: \( h_p = L_p(g^{p - 1} (\pmod p^2))^{-1} \pmod p \) \( h_q = L_q(g^{q - 1} (\pmod q^2))^{-1} \pmod q \) \( m_p = L_p(c^{p - 1} (\pmod p^2)) h_p \pmod p \) \( m_q = L_q(c^{q - 1} (\pmod q^2)) h_q \pmod q \) \( m = (m_p q (q^{-1} \pmod p) + m_q p (p^{-1} \pmod q)) (\pmod n) \)

If \( plaintext \leq \lfloor messagespace / 2 \rfloor \Rightarrow plaintext \geq 0 \) otherwise \( plaintext < 0 \Rightarrow plaintext = plaintext - messagespace \)

Implements SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >.

Definition at line 176 of file paillier.cpp.

void SeComLib::Core::Paillier::doPrecomputations ( )

privatevirtual

Precompute values for speedups.

Precompute \( h_p = L_p(g^{p - 1} (\pmod p^2))^{-1} \pmod p \) and \( h_q = L_q(g^{q - 1} (\pmod q^2))^{-1} \pmod q \) to speed up decryption via CRT

Speed optimizations for decryption: precompute \( p (p^{-1} \pmod q) \) and \( q (q^{-1} \pmod p) \)

Todo:: Catch a custom exception here

Populate the randomizer cache

Implements SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >.

Definition at line 304 of file paillier.cpp.

Paillier::Ciphertext SeComLib::Core::Paillier::EncryptIntegerNonrandom ( const BigInteger & plaintext ) const

virtual

Encrypt number without randomization.

Contains the "standard" and "shortcut" versions of the Paillier encryption algorithm without randomization.

Parameters

plaintext the plaintext integer

Returns: Encrypted ciphertext

"Standard" version: \( c = g^m r^n \pmod {n^2} \)
"Shortcut" version: \( c = (n*m + 1) r^n \pmod {n^2} \) The computation is performed in two steps:
encrypt data
randomize ciphertext

If \( plaintext < 0 \), we remap it to the second half of the message space

"Shortcut" version: \( c = (n*m + 1) \pmod {n^2} \)

Implements SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >.

Definition at line 214 of file paillier.cpp.

bool SeComLib::Core::Paillier::GenerateKeys ( )

virtual

Generate the public and private keys

Todo:: Implement a non-heuristic algorithm for insuring that \( n \) always has the specified length

Generates the Paillier cryptosystem keys.

Produces \( p \) and \( q \), each having half of the key length, and computes \( n = p q \), enforcing \( n \) to have the length specified by the key length.

Returns: Always true, for now

Set the length of primes p and q

If both are equal (highly unlikely) seek another prime

Compute \( n = p q \)

Need to guarantee that n always has the specified length? There should be a faster implementation for this...

"Shortcut" version:

Set \( g = n + 1 \)

\( \phi(n) \), \( \lambda \) and \( \mu \) are required by the "shortcut version" of the algorithm, but are no longer needed if decryption is done via CRT

Implements SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >.

Definition at line 105 of file paillier.cpp.

size_t SeComLib::Core::Paillier::GetMessageSpaceSize ( ) const

virtual

Returns the message space bit size.

Returns: The message space bit size.

Implements SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >.

Definition at line 283 of file paillier.cpp.

const BigInteger & SeComLib::Core::Paillier::GetMessageSpaceUpperBound ( ) const

virtual

Returns the message space upper bound.

Returns: \( n \)

Implements SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >.

Definition at line 276 of file paillier.cpp.

Paillier::Randomizer SeComLib::Core::Paillier::GetRandomizer ( ) const

virtual

Compute the random factor required for the encryption operation.

Generates a random number \( r \in \mathbb{Z}_n^* \) and computes \( r^n \pmod {n^2} \).

Computes \( r^n \pmod {n^2} \).

Returns: the randomizer

Implements SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >.

Definition at line 259 of file paillier.cpp.

BigInteger SeComLib::Core::Paillier::L	(	const BigInteger &	input,
		const BigInteger &	d
	)		const

private

L function evaluator.

Computes \( L(u) = \frac{u - 1}{d} \)

Parameters

input	the function variable
d	the divisor

Returns: L(input)

Definition at line 294 of file paillier.cpp.

Paillier::Ciphertext SeComLib::Core::Paillier::RandomizeCiphertext ( const Ciphertext & ciphertext ) const

virtual

Randomize encrypted number with a self-generated random value.

Computes \( c = c r^n \pmod {n^2} \).

Parameters

ciphertext the ciphertext integer

Returns: The randomized ciphertext

Implements SeComLib::Core::CryptoProvider< PaillierPublicKey, PaillierPrivateKey, PaillierCiphertext, PaillierRandomizer >.

Definition at line 269 of file paillier.cpp.

The documentation for this class was generated from the following files:

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation