paillierp.key
Class PaillierPrivateThresholdKey

java.lang.Object
  paillierp.key.PaillierKey
      paillierp.key.PaillierThresholdKey
          paillierp.key.PaillierPrivateThresholdKey

All Implemented Interfaces:

java.io.Serializable

public class PaillierPrivateThresholdKey
extends PaillierThresholdKey

A private key for the threshold Paillier scheme CS₁. This key is used to partially decrypt a ciphertext. At least PaillierThresholdKey.w cooperating decryption servers are needed in this scheme to produce a full decryption. The public information provided for in

The private key in this threshold scheme requires the following information to produce a partial decryption:

• The public values Δ and n provided for in PaillierThresholdKey
• i is the decryption server ID for this particular secret key
• s_i, which is the secret share particular to this server. This value is no other than f(i) for the (w-1)-degree polynomial f created by the key distributor.

Version:

0.9 03/25/10

Author:

James Garrity, Sean Hall

See Also:

PaillierKey, KeyGen, Serialized Form

Field Summary

protected int	id The server's id in the range of [1, l].
private static long	serialVersionUID This Serial ID
protected java.math.BigInteger	si The secret share.

Fields inherited from class paillierp.key.PaillierThresholdKey

delta, l, v, vi, w

Fields inherited from class paillierp.key.PaillierKey

k, MAX_KEY_SIZE, n, nPlusOne, ns, nSPlusOne, rnd

Constructor Summary

PaillierPrivateThresholdKey(java.math.BigInteger n, int l, java.math.BigInteger combineSharesConstant, int w, java.math.BigInteger v, java.math.BigInteger[] viarray, java.math.BigInteger si, int i, long seed)
Creates a new private key for the generalized Paillier threshold scheme from the given modulus n, for use on l decryption servers, w of which are needed to decrypt any message encrypted by using this private key.

PaillierPrivateThresholdKey(java.math.BigInteger n, int l, int w, java.math.BigInteger v, java.math.BigInteger[] viarray, java.math.BigInteger si, int i, long seed)
Creates a new private key for the generalized Paillier threshold scheme from the given modulus n, for use on l decryption servers, w of which are needed to decrypt any message encrypted by using this public key.

PaillierPrivateThresholdKey(byte[] b, long seed)
Creates a new private key using a byte encoding of a key.

Method Summary

boolean	canEncrypt() Describes if this key can be used to encrypt
int	getID() Returns the id of this private key.
java.math.BigInteger	getSi() Returns the secret share key which corresponds to this private key package.
byte[]	toByteArray() Encodes this key into a byte array.

Methods inherited from class paillierp.key.PaillierThresholdKey

getCombineSharesConstant, getDelta, getL, getThresholdKey, getV, getVi, getW

Methods inherited from class paillierp.key.PaillierKey

getK, getN, getNPlusOne, getNS, getNSPlusOne, getPublicKey, getRandomModN, getRandomModNSPlusOneStar, getRandomModNStar, getRnd, inModN, inModN, inModNS, inModNSPlusOne, inModNSPlusOneStar, inModNStar, inModNStar, isCiphertext, isPlaintext, setRnd, setRnd, updateRnd

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

si

protected java.math.BigInteger si

The secret share. This is unique among the L decryption servers.

id

protected int id

The server's id in the range of [1, l]. This identifies which verification key vi[id] to use.

Constructor Detail

PaillierPrivateThresholdKey

public PaillierPrivateThresholdKey(java.math.BigInteger n,
                                   int l,
                                   int w,
                                   java.math.BigInteger v,
                                   java.math.BigInteger[] viarray,
                                   java.math.BigInteger si,
                                   int i,
                                   long seed)

Creates a new private key for the generalized Paillier threshold scheme from the given modulus n, for use on l decryption servers, w of which are needed to decrypt any message encrypted by using this public key. The values v and vi correspond to the public values v and v_i=v^l!s_i needed to verify the zero knowledge proofs. si is the secret share for this decryption key, and i is the ID.

Parameters:

n - a safe prime product of p and q where p'=(p-1)/2 and a'=(a-1)/2 are also both primes

l - number of decryption servers

w - threshold of servers needed to successfully decrypt any ciphertext created by this public key. Note that w≤l/2.

v - a generator of a cyclic group of squares in Z^*_n²

viarray - array of verification keys where vi[i] is v^l!s_i where s_i is the private key for decryption server i

si - secret share for this server

i - ID of the decryption server (from 1 to l)

seed - a long integer needed to start a random number generator

PaillierPrivateThresholdKey

public PaillierPrivateThresholdKey(java.math.BigInteger n,
                                   int l,
                                   java.math.BigInteger combineSharesConstant,
                                   int w,
                                   java.math.BigInteger v,
                                   java.math.BigInteger[] viarray,
                                   java.math.BigInteger si,
                                   int i,
                                   long seed)

Creates a new private key for the generalized Paillier threshold scheme from the given modulus n, for use on l decryption servers, w of which are needed to decrypt any message encrypted by using this private key. The values v and vi correspond to the public values v and v_i=v^l!s_i needed to verify the zero knowledge proofs. si is the secret share for this decryption key, and i is the ID.

Parameters:

n - a safe prime product of p and q where p'=(p-1)/2 and a'=(a-1)/2 are also both primes

l - number of decryption servers

combineSharesConstant - precomputed value (4*l!)^-1 mod n

w - threshold of servers needed to successfully decrypt any ciphertext created by this public key. Note that w≤l/2.

v - a generator of a cyclic group of squares in Z^*_n²

viarray - array of verification keys where vi[i] is v^l!s_i where s_i is the private key for decryption server i

si - secret share for this server

i - ID of the decryption server (from 1 to l)

seed - a long integer needed to start a random number generator

PaillierPrivateThresholdKey

public PaillierPrivateThresholdKey(byte[] b,
                                   long seed)

Creates a new private key using a byte encoding of a key.

Parameters:

b - Byte array of the necessary values of this private key

seed - a long integer needed to start a random number generator

See Also:

toByteArray()

Method Detail

canEncrypt

public boolean canEncrypt()

Describes if this key can be used to encrypt

Overrides:

canEncrypt in class PaillierKey

Returns:

'true' if it can encrypt.

getSi

public java.math.BigInteger getSi()

Returns the secret share key which corresponds to this private key package. This was generated and given to this decryption server.

Returns:

secret share of this decryption server

getID

public int getID()

Returns the id of this private key. Mostly used to identify which verification key in PaillierThresholdKey.vi corresponds with this private key.

Returns:

ID of the decryption server's private key

toByteArray

public byte[] toByteArray()

Encodes this key into a byte array. As this is a public threshold key, the public modulo n, l, w, v, vi, id, and si will be encoded in that order. Further, before each BigInteger (except n) is the 4-byte equivalent to the size of the BigInteger for later parsing.

Overrides:

toByteArray in class PaillierThresholdKey

Returns:

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

See Also:

PaillierPrivateThresholdKey(byte[], long), BigInteger.toByteArray()