paillierp
Class AbstractPaillier

java.lang.Object
  paillierp.AbstractPaillier

Direct Known Subclasses:

Paillier, PaillierThreshold

public abstract class AbstractPaillier
extends java.lang.Object

An abstract class of the simple Paillier cryptosystem. This class is intended for use in both the Paillier and PaillierThreshold implementations of the generalized Paillier cryptosystem by Damgård.

This includes methods and fields common to both implementations, especially encryption and operations on ciphertexts; more specifically, the following operations are provided in this abstract class:

• encrypting messages,
• random encryptions of 0 and 1,
• randomizing a ciphertext,
• addition of two ciphertexts,
• multiplication of a ciphertext by a constant.

Any operations needing the decryption key is left to the specific cryptosystem and is not included in this class.

Note that every ciphertext and plaintext is a BigInteger.

Author:

Sean Hall, James Garrity

See Also:

Paillier, PaillierThreshold

Field Summary

protected boolean	decryptMode Boolean signifying that the variables for decryption are in place.
protected boolean	encryptMode Boolean signifying that the variables for encryption are in place.
protected PaillierKey	key Public Key allowing encryption.
protected java.lang.String	notReadyForDecryption String for error messages indicating that decryptMode is not set.
protected java.lang.String	notReadyForEncryption String for error messages indicating that encryptMode is not set.

Constructor Summary

AbstractPaillier()

Method Summary

java.math.BigInteger	add(java.math.BigInteger c1, java.math.BigInteger c2) Calculates E(m1+m2) given E(m1) and E(m2).
static java.math.BigInteger	add(java.math.BigInteger c1, java.math.BigInteger c2, java.math.BigInteger nsplus1) Calculates E(m1+m2) given E(m1) and E(m2), for a given cryptosystem CSs with public key n
java.math.BigInteger	encrypt(java.math.BigInteger m) Produces the random encryption of m.
java.math.BigInteger	encrypt(java.math.BigInteger m, java.math.BigInteger r) Produces the encryption E(m, r) using the message m and the randomization r in the Paillier cryptosystem.
static java.math.BigInteger	encrypt(java.math.BigInteger m, java.math.BigInteger r, java.math.BigInteger n, java.math.BigInteger ns, java.math.BigInteger nSPlusOne) Produces the encryption E(m, r).
static java.math.BigInteger	encrypt(java.math.BigInteger m, java.math.BigInteger r, PaillierKey key) Produces the encryption E(m, r).
static java.math.BigInteger	encrypt(java.math.BigInteger m, PaillierKey key) Produces a random encryption of m
java.math.BigInteger	encryptone() A random encryption of 1.
EncryptionZKP	encryptProof(java.math.BigInteger m) Produces a Zero Knowledge Proof of the encryption m
java.math.BigInteger	encryptzero() A random encryption of 0.
PaillierKey	getPublicKey() Returns the simple public key already in use in this instance of the cryptosystem.
java.math.BigInteger	multiply(java.math.BigInteger c1, java.math.BigInteger cons) Calculates E(cons*m) given E(m) and the constant cons, under our current public key.
static java.math.BigInteger	multiply(java.math.BigInteger c, java.math.BigInteger cons, java.math.BigInteger nSquare) Calculates E(cons*m) given E(m) and the constant cons, under the public key n for crypto system CSs.
java.math.BigInteger	multiply(java.math.BigInteger c1, long cons) Calculates E(cons*m) given E(m) and the constant cons, under our current public key.
MultiplicationZKP	multiplyProof(java.math.BigInteger c1, java.math.BigInteger cons) Calculates E(cons*m) given E(m) and the constant cons, under our current public key.
java.math.BigInteger	randomize(java.math.BigInteger c) Randomizes a given encryption by the given variable.
java.math.BigInteger	randomize(java.math.BigInteger c, java.math.BigInteger r) Randomizes a given encryption by the given variable.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

key

protected PaillierKey key

Public Key allowing encryption.

encryptMode

protected boolean encryptMode

Boolean signifying that the variables for encryption are in place.

decryptMode

protected boolean decryptMode

Boolean signifying that the variables for decryption are in place.

notReadyForEncryption

protected java.lang.String notReadyForEncryption

String for error messages indicating that encryptMode is not set.

notReadyForDecryption

protected java.lang.String notReadyForDecryption

String for error messages indicating that decryptMode is not set.

Constructor Detail

AbstractPaillier

public AbstractPaillier()

Method Detail

getPublicKey

public PaillierKey getPublicKey()

Returns the simple public key already in use in this instance of the cryptosystem. This includes the two values n and g needed for encryption. Returns null if no key has yet to be specified.

Returns:

the Paillier public key in use; null if the key is not initialized.

encrypt

public java.math.BigInteger encrypt(java.math.BigInteger m)

Produces the random encryption of m.

Parameters:

m - plaintext to be encrypted; must be less than n^s

Returns:

the encryption E(m,r) with a random r

encrypt

public java.math.BigInteger encrypt(java.math.BigInteger m,
                                    java.math.BigInteger r)

Produces the encryption E(m, r) using the message m and the randomization r in the Paillier cryptosystem.

Parameters:

m - plaintext to be encrypted; must be less than n^s

r - randomizer integer for the encryption; must be relatively prime to n and less than n

Returns:

the encryption E(m,r)

encrypt

public static java.math.BigInteger encrypt(java.math.BigInteger m,
                                           PaillierKey key)

Produces a random encryption of m

Parameters:

m - Message to be encoded; m<ns

key - Public Key doing the encoding

Returns:

The encryption E(m, r) using the public key key with random r

encrypt

public static java.math.BigInteger encrypt(java.math.BigInteger m,
                                           java.math.BigInteger r,
                                           PaillierKey key)

Produces the encryption E(m, r).

Parameters:

m - Message to be encoded; m<ns

r - Random number in Z^*_n

key - Public Key doing the encoding

Returns:

The encryption E(m, r) using the public key key

encrypt

public static java.math.BigInteger encrypt(java.math.BigInteger m,
                                           java.math.BigInteger r,
                                           java.math.BigInteger n,
                                           java.math.BigInteger ns,
                                           java.math.BigInteger nSPlusOne)

Produces the encryption E(m, r).

Parameters:

m - Message to be encoded; m<ns

r - Random number in Z^*_n

n - RSA modulus

ns - The value n^s

nSPlusOne - The value n^s+1

Returns:

The encryption E(m, r) using the public key n

encryptProof

public EncryptionZKP encryptProof(java.math.BigInteger m)

Produces a Zero Knowledge Proof of the encryption m

Parameters:

m - A message to be encrypted (must be less than n

Returns:

A non-interactive Zero Knowledge Proof that we in fact encrypted m

encryptzero

public java.math.BigInteger encryptzero()

A random encryption of 0.

Returns:

the encrypted value E(0,r) with random r

encryptone

public java.math.BigInteger encryptone()

A random encryption of 1.

Returns:

the encrypted value E(1,r) with random r

add

public java.math.BigInteger add(java.math.BigInteger c1,
                                java.math.BigInteger c2)

Calculates E(m₁+m₂) given E(m₁) and E(m₂).

Parameters:

c1 - the encryption E(m₁)

c2 - the encryption E(m₂)

Returns:

the encryption E(m₁+m₂)

add

public static java.math.BigInteger add(java.math.BigInteger c1,
                                       java.math.BigInteger c2,
                                       java.math.BigInteger nsplus1)

Calculates E(m₁+m₂) given E(m₁) and E(m₂), for a given cryptosystem CS_s with public key n

Parameters:

c1 - the encryption E(m₁) under the public key n

c2 - the encryption E(m₂) under the public key n

nsplus1 - n to the (s+1)th power

Returns:

the encryption E(m₁+m₂) under the supposed public key n in cryptosystem CS_s.

multiply

public java.math.BigInteger multiply(java.math.BigInteger c1,
                                     long cons)

Calculates E(cons*m) given E(m) and the constant cons, under our current public key.

Parameters:

c1 - the encryption E(m)

cons - the integer multiplicand

Returns:

the encryption E(cons*m)

multiply

public java.math.BigInteger multiply(java.math.BigInteger c1,
                                     java.math.BigInteger cons)

Calculates E(cons*m) given E(m) and the constant cons, under our current public key.

Parameters:

c1 - the encryption E(m)

cons - the integer multiplicand

Returns:

the encryption E(cons*m)

multiplyProof

public MultiplicationZKP multiplyProof(java.math.BigInteger c1,
                                       java.math.BigInteger cons)

Calculates E(cons*m) given E(m) and the constant cons, under our current public key. This method then returns a non-interactive Zero Knowledge Proof that the resulting encryption (i.e. E(cons*m)) is indeed the encryption of the multiplication of m by cons.

Parameters:

c1 - the encryption E(m)

cons - the integer multiplicand

Returns:

a ZKP of the encryption E(cons*m)

multiply

public static java.math.BigInteger multiply(java.math.BigInteger c,
                                            java.math.BigInteger cons,
                                            java.math.BigInteger nSquare)

Calculates E(cons*m) given E(m) and the constant cons, under the public key n for crypto system CS_s.

Parameters:

c - the encryption E(m) under the public key n

cons - the integer multiplicand

nSquare - n to the (s+1)th power

Returns:

the encryption E(cons*m) under the supposed public key n in cryptosystem CS_s

randomize

public java.math.BigInteger randomize(java.math.BigInteger c,
                                      java.math.BigInteger r)

Randomizes a given encryption by the given variable. Given E(m,r'), it returns E(m,r'*r).

Parameters:

c - the encryption E(m,r')

r - randomizer variable; must be relatively prime to n and less than n

Returns:

the encryption E(m,r'*r)

randomize

public java.math.BigInteger randomize(java.math.BigInteger c)

Randomizes a given encryption by the given variable. Given E(m,r), it returns E(m,r') for random r'.

Parameters:

c - the encryption E(m,r)

Returns:

the encryption E(m,r') for a new random r'