uheqiang/Homomorphic_Encryption

Contains Packages for ElGamal, Paillier, Goldweiser-Micali and DGK Homomorphic Encryption System. Also implements secure multiplication, division and comparison.

Homomorphic Encryption

Homomorphic Encryption is a Java library that implements the following partially homomorphic encryption systems:

• Paillier
• El-Gamal (Additive or multiplicative)
• Goldwasser-Micali
• DGK

As the partially homomorphic encryption systems only support addition with two ciphertexts, other protocols been appended to extend its functionality, in particular:

• Secure Multiplication
• Secure Division
• Secure Comparison

Installation

Please retrieve the JAR file from the latest release:
https://github.com/AndrewQuijano/Homomorphic_Encryption/tags

As this library uses Java 8, the JAR file can be imported into an Android project. If you want to review/edit the library, import the JAVA_PHE directory into a Eclipse project and edit as necessary. The Main.java folder only exists for testing and provide examples of how to use the library.

Usage

Import the packages as necessary. For basic usage please check Server.java in the test package for basic usage of these cryptography libraries. Please view Client.java and Server.java for an example how to compare encrypted numbers, secure multiplication, secure division, etc.

security.socialistmillionaire.alice

Initialize

alice Niu = new alice(new Socket("192.168.1.208", 9254));
// These Public Keys are made by Bob and automatically sent to Alice.
PaillierPublicKey pk = Niu.getPaillierPublicKey();
DGKPublicKey pubKey = Niu.getDGKPublicKey();
ElGamalPublicKey e_pk = Niu.getElGamalPublicKey();

Protocol1(x) See Protocol 1 in "Improving the DGK comparison protocol" in Alice section. Compare with plaintext value y Bob has.

• Parameters
  • plaintext (BigInteger)
• Returns
  • value (boolean) - x <= y
• Raises (HomomorphicException)
  • If the plaintext has more bits than what the DGK public key supports.

Protocol2(x, y) See Protocol 2 in "Improving the DGK comparison protocol" in Alice section.

• Parameters
  • x (BigInteger) - a Paillier/DGK encrypted value
  • y (BigInteger) - a Paillier/DGK encrypted value
• Returns
  • value (boolean) - x >= y
• Raises (HomomorphicException)
  • N/A

Protocol3(x) See Protocol 3 in "Improving the DGK comparison protocol" in Alice section. Compare with plaintext value y held by bob

• Parameters
  • x (BigInteger) - plaintext
• Returns
  • value (boolean) - x <= y
• Raises (HomomorphicException)
  • If the plaintext has more bits than what the DGK public key supports

Modified_Protocol3(x) See Protocol 3 in "Correction to 'Improving the DGK comparison protocol'" in Alice section. View the sub-protocol.

• Parameters
  • x (BigInteger) - plaintext
• Returns
  • value (boolean) - x <= y
• Raises (HomomorphicException)
  • N/A

Protocol4(x, y) See Protocol 3 in "Correct to 'Improving the DGK comparison protocol'" in Alice section.

• Parameters
  • x (BigInteger) - Paillier or DGK encrypted value
  • y (BigInteger) - Paillier or DGK encrypted value
• Returns
  • value (boolean) - x >= y
• Raises (HomomorphicException) *

BigInteger x = new BigInteger("50");
BigInteger y = new BigInteger("51");

// Note: Assume bob is sharing y = new BigIntger("55");
Niu.Protocol1(x); // TRUE, X <= Y
Niu.Protocol3(x);// TRUE X <= Y
Niu.Modified_Protocol3(x); // TRUE X <= Y

// Note: Protocol 2 only works with Paillier encrypted values!
// Note: Protocol 2/4 works with Paillier/DGK encrypted values!
x = PaillierCipher.encrypt(x, pk); 
y = PaillierCipher.encrypt(y, pk);
Niu.Protocol2(x, y); // FALSE, b.c X >= Y is FALSE
Niu.Protocol4(x, y); // FALSE: b.c X >= Y is FALSE

division(x, y) Please review Protocol 2 in the "Encrypted Integer Division" paper by Thjis Veugen

• Parameters
  • x (BigInteger) - Paillier or DGK encrypted value
  • d (BigInteger) - plaintext value
• Returns
  • ciphertext (BigInteger) - x/d
• Raises (HomomorphicException)
  • Constraints: 0 <= x <= N * 2^{-sigma} and 0 <= d < N

multiplication(x, y)

• Parameters
  • x (BigInteger) - Paillier or DGK encrypted value
  • y (BigInteger) - Paillier or DGK encrypted value
• Returns
  • ciphertext (BigInteger) - x * y
• Raises (HomomorphicException)
  • Constraints: 0 <= x <= N * 2^{-sigma} and 0 <= d < N

bubbleSort(arr)

• Parameters
  • arr (BigInteger) - List of Paillier or DGK encrypted value
• Returns
  • N/A - arr is list of sorted encrypted values from low to high
• Raises (HomomorphicException)
  • N/A

getKMax(arr, k)

• Parameters
  • arr (List) - List of Paillier or DGK encrypted value
  • k - get number of k largest encrypted numbers
• Returns
  • a (List) - new array of size k sorted from low to high
• Raises (HomomorphicException)
  • N/A

getKMin(arr, k)

• Parameters
  • arr (List) - List of Paillier or DGK encrypted value
  • k - get number of k smallest encrypted numbers
• Returns
  • a (List) - new array of size k sorted from low to high
• Raises (HomomorphicException)
  • N/A

security.socialistmillionaire.bob

Initialize

// Build all Key Pairs
GMKeyPairGenerator gmg = new GMKeyPairGenerator();
gmg.initialize(KEY_SIZE, null);
KeyPair gm = gmg.generateKeyPair();

PaillierKeyPairGenerator p = new PaillierKeyPairGenerator();
p.initialize(KEY_SIZE, null);
KeyPair pe = p.generateKeyPair();

ElGamalKeyPairGenerator pg = new ElGamalKeyPairGenerator();
// NULL -> ADDITIVE
// NOT NULL -> MULTIPLICATIVE
pg.initialize(KEY_SIZE, new SecureRandom());
KeyPair el_gamal = pg.generateKeyPair();
	
bob_socket = new ServerSocket(9254);
bob_client = bob_socket.accept();
// Note: Alice automatically gets the public keys!
andrew = new bob(bob_client, pe, DGK, el_gamal);

Protocol1(y) See Protocol 1 in "Improving the DGK comparison protocol" in Bob section. Compare with plaintext value y Bob has.

• Parameters
  • plaintext (BigInteger)
• Returns
  • value (boolean) - x <= y
• Raises (HomomorphicException)
  • If the plaintext has more bits than what the DGK public key supports.

Protocol2() See Protocol 2 in "Improving the DGK comparison protocol" in Bob section.

• Parameters
  • N/A
• Returns
  • value (boolean) - x >= y
• Raises (HomomorphicException)
  • N/A

Protocol3(y) See Protocol 3 in "Improving the DGK comparison protocol" in Bob section. Compare with plaintext value y held by bob

• Parameters
  • y (BigInteger) - plaintext
• Returns
  • value (boolean) - x <= y
• Raises (HomomorphicException)
  • If the plaintext has more bits than what the DGK public key supports

Modified_Protocol3(y) See Protocol 3 in "Correction to 'Improving the DGK comparison protocol'" in Bob section. View the sub-protocol.

• Parameters
  • y (BigInteger) - plaintext
• Returns
  • value (boolean) - x <= y
• Raises (HomomorphicException)
  • N/A

Protocol4() See Protocol 3 in "Correct to 'Improving the DGK comparison protocol'" in Bob section.

• Parameters
  • N/A
• Returns
  • value (boolean) - x >= y
• Raises (HomomorphicException) *

division(x, y) Please review Protocol 2 in the "Encrypted Integer Division" paper by Thjis Veugen

• Parameters
  • d (BigInteger) - plaintext value
• Returns
  • N/A
• Raises (HomomorphicException)
  • Constraints: 0 <= x <= N * 2^{-sigma} and 0 <= d < N

multiplication() Please review 'Correction of a Secure Comparison Protocol for Encrypted Integers in IEEE WIFS 2012 (Short Paper)' by Mau et al., page 3, an outsourced multiplication section.

• Parameters
  • N/A
• Returns
  • N/A
• Raises (HomomorphicException)
  • Constraints: 0 <= x <= N * 2^{-sigma} and 0 <= d < N

security.DGK

Generate DGK Keys

int KEY_SIZE = 1024; //number of bits
SecureRandom r = new SecureRandom();
DGKKeyPairGenerator p = new DGKKeyPairGenerator();
p.initialize(KEY_SIZE, r);
KeyPair pe = p.generateKeyPair();
DGKPublicKey pk = (DGKPublicKey) pe.getPublic();
DGKPrivateKey sk = (DGKPrivateKey) pe.getPrivate();

encrypt(plaintext, pk) Encrypt a plain-text BigInteger using the DGK Cryptography system.

• Parameters
  • plaintext (long)
  • pk (DGKPublicKey)
• Returns
  • ciphertext (BigInteger)
• Raises (HomomorphicException)
  • If the plaintext is negative or exceeds plaintext space that can be handled by the DGK Public Key, this exception will be generated.

decrypt(ciphertext, sk) Decrypt a cipher-text BigInteger using the DGK Cryptography system.

• Parameters
  • ciphertext (BigInteger)
  • sk (DGKPrivateKey)
• Returns
  • plaintext (long)
• Raises (HomomorphicException)
  • If the ciphertext is negative or exceeds ciphertext space that can be handled by the DGK Private Key, this exception will be generated.

BigInteger c = DGKOperations.encrypt(10, pk);
long d = DGKOperations.decrypt(c, pk); // d = 10

add(ciphertext1, ciphertext2, pk) Add the results of both ciphertexts.

• Parameters
  • ciphertext1 (BigInteger) - a DGK ciphertext
  • ciphertext2 (BigInteger) - a second DGK ciphertext
  • pk (DGKPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of both ciphertexts
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the sum of the ciphertexts exceeds the plaintext space of supported by the DGK public key, the sum is subject to mod N, the size of the plaintext space.

add_plaintext(ciphertext, plaintext, pk) Add the value in plaintext within the ciphertext. This is much faster than regular add as you save an encryption operation.

• Parameters
  • ciphertext (BigInteger) - a DGK ciphertext
  • plaintext (BigInteger) - a BigInteger plaintext
  • pk (DGKPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of both the ciphertext and plaintext
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the sum of the ciphertexts exceeds the plaintext space of supported by the DGK public key, the sum is subject to mod u, the size of the plaintext space.

// Addition
BigInteger c = DGKOperations.encrypt(10, pk);
c = DGKOperations.add(c, c, pk); 
// c = 10 + 10 = 20. Notice both arguments need to be encrypted. c is still encrypted!
// Scalar addition
BigInteger d = DGKOperations.encrypt(10, pk);
d = DGKOperations.add_plaintext(d, 10, pk);
// d = 10 + 10 = 20. The second argument must be a plaintext if using plaintext addition! 
// d is still encrypted!

subtract(ciphertext1, ciphertext2, pk) Subtract the results of both ciphertexts.

• Parameters
  • ciphertext1 (BigInteger) - a DGK ciphertext
  • ciphertext2 (BigInteger) - a second DGK ciphertext
  • pk (DGKPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted subtraction of ciphertext1 and ciphertext2.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the value encrypted in ciphertext2 is greater than the value encrypted in ciphertext1, the value is not negative, it would be congruent to a positive value mod u when decrypted.

subtract_plaintext(ciphertext, plaintext, pk) Subtract the value in plaintext with the ciphertext. This is much faster than regular subtraction as you save an encryption operation.

• Parameters
  • ciphertext (BigInteger) - a DGK ciphertext
  • plaintext (BigInteger) - a BigInteger plaintext
  • pk (DGKPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of both the ciphertext and plaintext
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the value encrypted in ciphertext2 is greater than the value encrypted in ciphertext1, the value is not negative, it would be congruent to a positive value mod u when decrypted.

c = DGKOperations.encrypt(10, pk);
c = DGKOperations.multiply(c, 10, pk);
// c = 10 * 10 = 100. 
// First argument is cipher-text, second is plain-text value

multiply(ciphertext, plaintext, pk) Multiply the encrypted value in the ciphertext with the plaintext

• Parameters
  • ciphertext (BigInteger) - a DGK ciphertext
  • plaintext (BigInteger) - a plaintext BigInteger
  • pk (DGKPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted multilpication of ciphertext and plaintext.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the product explains the plaintext space, it is subject to mod u, the plain-text space.

divide(ciphertext, plaintext, pk) Divide the encrypted value in the ciphertext with the plaintext

• Parameters
  • ciphertext (BigInteger) - a DGK ciphertext
  • plaintext (BigInteger) - a plaintext BigInteger
  • pk (DGKPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted ciphertext divided by the plaintext.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If you do this, you need to make sure that the plaintext divides the value encrypted in the ciphertext! Otherwise you will get a horribly wrong answer! You should use the Division Protocol if you can't make this gurantee on the Sociallist Millionaire's package!

security.elgamal

Generate ElGamal Keys

int KEY_SIZE = 1024; //number of bits
SecureRandom r = new SecureRandom();
ElGamalKeyPairGenerator p = new ElGamalKeyPairGenerator();
p.initialize(KEY_SIZE, r);
KeyPair pe = p.generateKeyPair();
ElGamalPublicKey pk = (ElGamalPublicKey) pe.getPublic();
ElGamalPrivateKey sk = (ElGamalPrivateKey) pe.getPrivate();

encrypt(plaintext, pk) Encrypt a plain-text BigInteger using the ElGamal Cryptography system.

• Parameters
  • plaintext (BigInteger)
  • pk (ElGamalPublicKey)
• Returns
  • ciphertext (ElGamal_Ciphertext)
• Raises (HomomorphicException)
  • If the plaintext is negative or exceeds plaintext space that can be handled by the ElGamal Public Key, this exception will be generated.

decrypt(ciphertext, sk) Decrypt a cipher-text BigInteger using the ElGamal Cryptography system.

• Parameters
  • ciphertext (ElGamal_Ciphertext)
  • sk (ElGamalPrivateKey)
• Returns
  • plaintext (BigInteger)
• Raises (HomomorphicException)
  • If the ciphertext is negative or exceeds ciphertext space that can be handled by the ElGamal Private Key, this exception will be generated.

BigInteger c = PaillierCipher.encrypt(BigInteger.TEN, pk);
c = PaillierCipher.decrypt(c, pk); // c = 10

add(ciphertext1, ciphertext2, pk) Add the results of both ciphertexts.

• Parameters
  • ciphertext1 (ElGamal_ciphertext) - a ElGamal ciphertext
  • ciphertext2 (ElGamal_ciphertext) - a second ElGamal ciphertext
  • pk (ElGamalPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of both ciphertexts
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the sum of the ciphertexts exceeds the plaintext space of supported by the Paillier public key, the sum is subject to mod N, the size of the plaintext space.

add_plaintext(ciphertext, plaintext, pk) Add the value in plaintext within the ciphertext. This is much faster than regular add as you save an encryption operation.

• Parameters
  • ciphertext (ElGamal_ciphertext) - a ElGamal ciphertext
  • plaintext (BigInteger) - a BigInteger plaintext
  • pk (ElGamalPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of both the ciphertext and plaintext
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the sum of the ciphertexts exceeds the plaintext space of supported by the ElGamal public key, the sum is subject to mod N, the size of the plaintext space.

// Addition
ElGamal_Ciphertext c = ElGamalCipher.encrypt(BigInteger.TEN, pk);
c = ElGamalCipher.add(c, c, pk); 
// c = 10 + 10 = 20. Notice both arguments need to be encrypted. c is still encrypted!
// Scalar addition
ElGamal_Ciphertext d = ElGamalCipher.encrypt(BigInteger.TEN, pk);
d = ElGamalCipher.add_plaintext(d, BigInteger.TEN, pk);
// d = 10 + 10 = 20. The second argument must be a plaintext if using plaintext addition! 
// d is still encrypted!

subtract(ciphertext1, ciphertext2, pk) Subtract the results of both ciphertexts.

• Parameters
  • ciphertext1 (ElGamal_ciphertext) - a ElGamal ciphertext
  • ciphertext2 (ElGamal_ciphertext) - a second ElGamal ciphertext
  • pk (ElGamalPublicKey)
• Returns
  • ciphertext (ElGamal_ciphertext) - This ciphertext is the encrypted subtraction of ciphertext1 and ciphertext2.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the value encrypted in ciphertext2 is greater than the value encrypted in ciphertext1, the value is not negative, it would be congruent to a positive value mod N when decrypted.

subtract_plaintext(ciphertext, plaintext, pk) Subtract the value in plaintext with the ciphertext. This is much faster than regular subtraction as you save an encryption operation.

• Parameters
  • ciphertext (ElGamal_ciphertext) - a ElGamal ciphertext
  • plaintext (BigInteger) - a BigInteger plaintext
  • pk (PaillierPublicKey)
• Returns
  • ciphertext (ElGamal_ciphertext) - This ciphertext is the encrypted sum of both the ciphertext and plaintext
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the value encrypted in ciphertext2 is greater than the value encrypted in ciphertext1, the value is not negative, it would be congruent to a positive value mod N when decrypted.

c = ElGamalCipher.encrypt(BigInteger.TEN, pk);
c = ElGamalCipher.multiply(c, BigInteger.TEN, pk);
// c = 10 * 10 = 100. 
// First argument is cipher-text, second is plain-text value

multiply(ciphertext, plaintext, pk) Multiply the encrypted value in the ciphertext with the plaintext

• Parameters
  • ciphertext (ElGamal_ciphertext) - a ElGamal ciphertext
  • plaintext (BigInteger) - a plaintext BigInteger
  • pk (ElGamalPublicKey)
• Returns
  • ciphertext (ElGamal_ciphertext) - This ciphertext is the encrypted multilpication of ciphertext and plaintext.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the product explains the plaintext space, it is subject to mod N, the plain-text space.

divide(ciphertext, plaintext, pk) Divide the encrypted value in the ciphertext with the plaintext

• Parameters
  • ciphertext (ElGamal_ciphertext) - a ElGamal ciphertext
  • plaintext (BigInteger) - a plaintext BigInteger
  • pk (ElGamalPublicKey)
• Returns
  • ciphertext (ElGamal_ciphertext) - This ciphertext is the encrypted ciphertext divided by the plaintext.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If you do this, you need to make sure that the plaintext divides the value encrypted in the ciphertext! Otherwise you will get a horribly wrong answer! You should use the Division Protocol if you can't make this gurantee on the Sociallist Millionaire's package!

security.gm

Generate Goldwasser-Micali Keys

GMKeyPairGenerator gmg = new GMKeyPairGenerator();
gmg.initialize(KEY_SIZE, null);
KeyPair gm = gmg.generateKeyPair();
GMPublicKey gm_pk = (GMPublicKey) gm.getPublic();
GMPrivateKey gm_sk = (GMPrivateKey) gm.getPrivate();

encrypt(plaintext, pk) Encrypt a plain-text BigInteger using the Goldwasser-Micali Cryptography system.

• Parameters
  • plaintext (BigInteger)
  • pk (GMPublicKey)
• Returns
  • ciphertext (List)
• Raises (HomomorphicException)
  • N/A

decrypt(ciphertext, sk) Decrypt a cipher-text using the Goldwasser-Micali Cryptography system.

• Parameters
  • ciphertext (List)
  • sk (GMPrivateKey)
• Returns
  • plaintext (BigInteger)
• Raises (HomomorphicException)
  • N/A

List<BigInteger> c = GMCipher.encrypt(BigInteger.TEN, gm_pk);
BigInteger d = GMCipher.decrypt(c, pk); // c = 10

xor(ciphertext1, ciphertext2, pk) XOR both ciphertexts.

• Parameters
  • ciphertext1 (List) - a Goldwasser-Micali ciphertext
  • ciphertext2 (List) - a second Goldwasser-Micali ciphertext
  • pk (GMPublicKey)
• Returns
  • ciphertext (List) - This ciphertext is the encrypted xor of both ciphertexts
• Raises (HomomorphicException)
  • If both ciphertexts dont have the same number of bits, an exception will be thrown. **

security.paillier

Generate Paillier Keys

int KEY_SIZE = 1024; //number of bits
SecureRandom r = new SecureRandom();
PaillierKeyPairGenerator p = new PaillierKeyPairGenerator();
p.initialize(KEY_SIZE, r);
KeyPair pe = p.generateKeyPair();
PaillierPublicKey pk = (PaillierPublicKey) pe.getPublic();
PaillierPrivateKey sk = (PaillierPrivateKey) pe.getPrivate();

encrypt(plaintext, pk) Encrypt a plain-text BigInteger using the Paillier Cryptography system.

• Parameters
  • plaintext (BigInteger)
  • pk (PaillierPublicKey)
• Returns
  • ciphertext (BigInteger)
• Raises (HomomorphicException)
  • If the plaintext is negative or exceeds plaintext space that can be handled by the Paillier Public Key, this exception will be generated.

decrypt(ciphertext, sk) Decrypt a cipher-text BigInteger using the Paillier Cryptography system.

• Parameters
  • ciphertext (BigInteger)
  • sk (PaillierPrivateKey)
• Returns
  • plaintext (BigInteger)
• Raises (HomomorphicException)
  • If the ciphertext is negative or exceeds ciphertext space that can be handled by the Paillier Private Key, this exception will be generated.

BigInteger c = PaillierCipher.encrypt(BigInteger.TEN, pk);
c = PaillierCipher.decrypt(c, pk); // c = 10

add(ciphertext1, ciphertext2, pk) Add the results of both ciphertexts.

• Parameters
  • ciphertext1 (BigInteger) - a Paillier ciphertext
  • ciphertext2 (BigInteger) - a second Paillier ciphertext
  • pk (PaillierPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of both ciphertexts
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the sum of the ciphertexts exceeds the plaintext space of supported by the Paillier public key, the sum is subject to mod N, the size of the plaintext space.

add_plaintext(ciphertext, plaintext, pk) Add the value in plaintext within the ciphertext. This is much faster than regular add as you save an encryption operation.

• Parameters
  • ciphertext (BigInteger) - a Paillier ciphertext
  • plaintext (BigInteger) - a BigInteger plaintext
  • pk (PaillierPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of both the ciphertext and plaintext
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the sum of the ciphertexts exceeds the plaintext space of supported by the Paillier public key, the sum is subject to mod N, the size of the plaintext space.

// Addition
BigInteger c = PaillierCipher.encrypt(BigInteger.TEN, pk);
c = PaillierCipher.add(c, c, pk); 
// c = 10 + 10 = 20. Notice both arguments need to be encrypted. c is still encrypted!
// Scalar addition
BigInteger d = PaillierCipher.encrypt(BigInteger.TEN, pk);
d = PaillierCipher.add_plaintext(d, BigInteger.TEN, pk);
// d = 10 + 10 = 20. The second argument must be a plaintext if using plaintext addition! 
// d is still encrypted!

subtract(ciphertext1, ciphertext2, pk) Subtract the results of both ciphertexts.

• Parameters
  • ciphertext1 (BigInteger) - a Paillier ciphertext
  • ciphertext2 (BigInteger) - a second Paillier ciphertext
  • pk (PaillierPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted subtraction of ciphertext1 and ciphertext2.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the value encrypted in ciphertext2 is greater than the value encrypted in ciphertext1, the value is not negative, it would be congruent to a positive value mod N when decrypted.

subtract_plaintext(ciphertext, plaintext, pk) Subtract the value in plaintext with the ciphertext. This is much faster than regular subtraction as you save an encryption operation.

• Parameters
  • ciphertext (BigInteger) - a Paillier ciphertext
  • plaintext (BigInteger) - a BigInteger plaintext
  • pk (PaillierPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of both the ciphertext and plaintext
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the value encrypted in ciphertext2 is greater than the value encrypted in ciphertext1, the value is not negative, it would be congruent to a positive value mod N when decrypted.

c = PaillierCipher.encrypt(BigInteger.TEN, pk);
c = PaillierCipher.multiply(c, BigInteger.TEN, pk);
// c = 10 * 10 = 100. 
// First argument is cipher-text, second is plain-text value

multiply(ciphertext, plaintext, pk) Multiply the encrypted value in the ciphertext with the plaintext

• Parameters
  • ciphertext (BigInteger) - a Paillier ciphertext
  • plaintext (BigInteger) - a plaintext BigInteger
  • pk (PaillierPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted multilpication of ciphertext and plaintext.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If the product explains the plaintext space, it is subject to mod N, the plain-text space.

divide(ciphertext, plaintext, pk) Divide the encrypted value in the ciphertext with the plaintext

• Parameters
  • ciphertext (BigInteger) - a Paillier ciphertext
  • plaintext (BigInteger) - a plaintext BigInteger
  • pk (PaillierPublicKey)
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted ciphertext divided by the plaintext.
• Raises (HomomorphicException)
  • N/A
• Warning:
  • If you do this, you need to make sure that the plaintext divides the value encrypted in the ciphertext! Otherwise you will get a horribly wrong answer! You should use the Division Protocol if you can't make this gurantee on the Sociallist Millionaire's package!

sum(ciphertext, pk) Compute the sum of all ciphertexts

• Parameters
  • ciphertext (List) - a List of Paillier ciphertexts
  • pk (PaillierPublicKey) - used to sum all ciphertexts
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of all values in the list of ciphertext
• Raises (HomomorphicException)
  • N/A

sum(ciphertext, pk, limit) Compute the sum of all ciphertexts from 0 up to the index specified by limit.

• Parameters
  • ciphertext (List) - a List of Paillier ciphertexts
  • pk (PaillierPublicKey) - used to sum all ciphertexts
  • limit (int) - index to sum up to.
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of all values in the list of ciphertext up to the limit.
• Raises (HomomorphicException)
  • N/A

sum_product(ciphertext, plaintext pk) Compute the product of each ciphertext and plaintext. Then sum all the products.

• Parameters
  • ciphertext (List) - a List of Paillier ciphertexts
  • plaintext (List) - a List of plaintext values
  • pk (PaillierPublicKey) - used to compute sum and product
• Returns
  • ciphertext (BigInteger) - This ciphertext is the encrypted sum of products of the list of ciphertext and plaintexts.
• Raises (HomomorphicException)
  • If the size of the list of ciphertexts and plaintext are not equal.

sign(plaintext, sk) Sign the plaintext using a Paillier Private Key.

• Parameters
  • plaintext (BigInteger) - plaintext
  • sk (PaillierPrivateKey) - used to sign the BigInteger
• Returns
  • signature (BigInteger) - The signed BigInteger
• Raises (HomomorphicException)
  • N/A

verify(plaintext, signature, pk) Verify the signature using the Paillier Public Key

• Parameters
  • plaintext (BigInteger) - plaintext that is suppossedly signed
  • signature (BigInteger) - signed bytes with its corresponding PaillierPrivateKey
  • pk (PaillierPublicKey) - used to verify the signature
• Returns
  • valid (boolean) - true if valid, false if not valid
• Raises (HomomorphicException)
  • N/A

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

Authors and acknowledgment

Code author: Andrew Quijano

All papers and protocols used in the code have been published in various cryptography journals. Please view the Papers directory to read the paper this library code implements. If you use this library, please cite the papers in the Papers directory.

Also, please cite the paper: A. Quijano and K. Akkaya, "Server-Side Fingerprint-Based Indoor Localization Using Encrypted Sorting," 2019 IEEE 16th International Conference on Mobile Ad Hoc and Sensor Systems Workshops (MASSW), Monterey, CA, USA, 2019, pp. 53-57, doi: 10.1109/MASSW.2019.00017.

https://arxiv.org/abs/2008.11612

The work to create this repository was initially funded by the US NSF REU Site at FIU under the grant number REU CNS-1461119.

License

MIT

Project status

The project is currently fully tested. To see an example how to use it, unzip the example.zip file and play the video. Currently, the strech goal is to implement certificates using the Bouncy Castle API for these homomorphic encryption systems.