paillierp.zkp
Class DecryptionZKP

java.lang.Object
  paillierp.zkp.ZKP
      paillierp.zkp.DecryptionZKP

All Implemented Interfaces:

java.io.Serializable

public class DecryptionZKP
extends ZKP

A non-interactive Zero Knowledge Proof that some partial decryption was done. (Note that this is only for the threshold version of the scheme.) This is essentially a protocol for the equality of discrete logs, i.e. given u, u', v, v', prove that log_u(u') = log_v(v'). This Zero Knowledge Proof will correctly validate whether the ciphertext c was indeed raised to the 2Δs_i power by comparing it with the public verification v_i. This checks that log_c⁴(c_i²) = log_v(v_i). Recall that v_i = v^Δs_i.

The protocol is given on pp. 16-17 in Generalization of Paillier's Public-Key System with Applications to Electronic Voting by Damgård et al.

Author:

Murat Kantarcioglu, Sean Hall, James Garrity

See Also:

PaillierThreshold, Serialized Form

Field Summary

protected java.math.BigInteger	c The original ciphertext.
protected java.math.BigInteger	c4 The ciphtertext to the fourth power.
protected PartialDecryption	ci This share's decryption of c.
protected java.math.BigInteger	ci2 The share's decryption of c, but squared, for the protocol.
protected java.math.BigInteger	e The hash of the correctness.
protected java.math.BigInteger	nSPlusOne The public key value.
private static long	serialVersionUID This Serial ID
protected java.math.BigInteger	v The overall verification number.
protected java.math.BigInteger	vi The share's verification number.
protected java.math.BigInteger	z The value necessary to check the correctness of this decryption.

Fields inherited from class paillierp.zkp.ZKP

hashFunction

Constructor Summary

DecryptionZKP(byte[] b)
Creates an instance of the Zero Knowledge Proof of decryption from a byte array which does have the key encoded.

DecryptionZKP(byte[] b, java.math.BigInteger nSPlusOne, java.math.BigInteger v, java.math.BigInteger vi)
Creates an instance of the Zero Knowledge Proof from a byte array (which does not have the key) and the values necessary for verification.

DecryptionZKP(byte[] b, PaillierThresholdKey pubkey)
Creates an instance of the Zero Knowledge Proof from a byte array (which does not have the key) and a public key.

DecryptionZKP(PaillierPrivateThresholdKey deckey, java.math.BigInteger c)
Creates an instance of the Zero Knoweledge Proof and partial decryption.

Method Summary

java.math.BigInteger	getC() Returns the original ciphertext.
int	getID() Returns the ID of the key used to make this partial decryption.
PartialDecryption	getPartialDecryption()
java.math.BigInteger	getValue() The partial decryption intended to be delivered.
byte[]	toByteArray() Encodes this ZKP into a byte array.
byte[]	toByteArrayNoKey() Encodes this ZKP into a byte array.
boolean	verify() Evaluates the truth of this partial decryption.
boolean	verify(java.math.BigInteger origc) Evaluates the truth of this partial decryption as a partial decryption of origc.
boolean	verifyKey(PaillierThresholdKey origkey) Verifies that the values used in this Zero Knowledge Proof corresponds to the given key.

Methods inherited from class paillierp.zkp.ZKP

hash

Methods inherited from class java.lang.Object

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

Field Detail

serialVersionUID

private static final long serialVersionUID

This Serial ID

See Also:

Constant Field Values

e

protected java.math.BigInteger e

The hash of the correctness.

z

protected java.math.BigInteger z

The value necessary to check the correctness of this decryption.

c

protected java.math.BigInteger c

The original ciphertext.

c4

protected java.math.BigInteger c4

The ciphtertext to the fourth power.

ci

protected PartialDecryption ci

This share's decryption of c. That is, ci = c^2Δs_i.

ci2

protected java.math.BigInteger ci2

The share's decryption of c, but squared, for the protocol.

nSPlusOne

protected java.math.BigInteger nSPlusOne

The public key value. Needed for verifying values.

v

protected java.math.BigInteger v

The overall verification number. Needed for verifying values.

vi

protected java.math.BigInteger vi

The share's verification number. Needed for verifying values.

Constructor Detail

DecryptionZKP

public DecryptionZKP(byte[] b)

Creates an instance of the Zero Knowledge Proof of decryption from a byte array which does have the key encoded.

Parameters:

b - byte array of the necessary values for a ZKP

Throws:

java.lang.IllegalArgumentException - if it detects that some corruption has occured, for example, if the "size of next BigInteger" field is a larger number than typical causing out of bounds issues.

See Also:

toByteArray()

DecryptionZKP

public DecryptionZKP(byte[] b,
                     java.math.BigInteger nSPlusOne,
                     java.math.BigInteger v,
                     java.math.BigInteger vi)

Creates an instance of the Zero Knowledge Proof from a byte array (which does not have the key) and the values necessary for verification.

Parameters:

b - byte array of the necessary values for a ZKP

nSPlusOne - the public key modulus n^s+1

v - the public key verifier for partial decryptions

vi - the public key verifier for partial decryptions from this particular server

See Also:

toByteArrayNoKey()

DecryptionZKP

public DecryptionZKP(byte[] b,
                     PaillierThresholdKey pubkey)

Creates an instance of the Zero Knowledge Proof from a byte array (which does not have the key) and a public key.

Parameters:

b - byte array of the necessary values for a ZKP

pubkey - public Paillier key to provide further recurring values for a ZKP

See Also:

toByteArrayNoKey()

DecryptionZKP

public DecryptionZKP(PaillierPrivateThresholdKey deckey,
                     java.math.BigInteger c)

Creates an instance of the Zero Knoweledge Proof and partial decryption. By creating a hash of values including the partial decryption, this sets up the variables for a recomputation of the hash to verify the truth that c_i is indeed c partially decrypted.

Parameters:

deckey - Private key used to generate a partial decryption

c - Ciphertext to be decrypted

Method Detail

verify

public boolean verify()

Evaluates the truth of this partial decryption. By recomputing the hash, it checks to see that indeed c_i was computed correctly.

Specified by:

verify in class ZKP

Returns:

The truth of the computation of c_i

verify

public boolean verify(java.math.BigInteger origc)

Evaluates the truth of this partial decryption as a partial decryption of origc. By recomputing the hash, it checks to see that indeed c_i was computed correctly from origc.

Parameters:

origc - Original Ciphertext.

Returns:

The truth of the computation of c_i as coming from origc.

verifyKey

public boolean verifyKey(PaillierThresholdKey origkey)

Verifies that the values used in this Zero Knowledge Proof corresponds to the given key.

Parameters:

origkey - Original key

Returns:

The truth of the computation of c_i as being encrypted by origkey

getC

public java.math.BigInteger getC()

Returns the original ciphertext.

Returns:

The ciphertext of which this is a partial decryption

getID

public int getID()

Returns the ID of the key used to make this partial decryption.

Returns:

The ID of the decryption server generating this partial decryption

getValue

public java.math.BigInteger getValue()

The partial decryption intended to be delivered.

Specified by:

getValue in class ZKP

Returns:

A partial decryption c_i

See Also:

PaillierThreshold.decrypt(BigInteger)

getPartialDecryption

public PartialDecryption getPartialDecryption()

toByteArray

public byte[] toByteArray()

Encodes this ZKP into a byte array. All of the necessary values (including the public key values) needed to verify the veracity of this partial decryption are encoded. Before each BigInteger (except n) is the 4-byte equivalent to the size of the BigInteger for later parsing.

Specified by:

toByteArray in class ZKP

Returns:

a byte array containing the most necessary values of this ZKP. A byte array of size 0 is returned if the byte array would be too large.

See Also:

DecryptionZKP(byte[]), BigInteger.toByteArray()

toByteArrayNoKey

public byte[] toByteArrayNoKey()

Encodes this ZKP into a byte array. All of the necessary values (besides the public key values) needed to verify the veracity of this partial decryption are encoded. Before each BigInteger (except n) is the 4-byte equivalent to the size of the BigInteger for later parsing.

Specified by:

toByteArrayNoKey in class ZKP

Returns:

a byte array containing the most necessary values of this ZKP. A byte array of size 0 is returned if the byte array would be too large.

See Also:

DecryptionZKP(byte[], PaillierThresholdKey), BigInteger.toByteArray()