paillierp.key
Class PaillierThresholdKey

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

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

PaillierPrivateThresholdKey

public class PaillierThresholdKey
extends PaillierKey

A public key for the threshold Paillier cryptosystem CS₁. Provides encryption credentials to encrypt, as well as the public variables and values needed for the threshold variant of the Paillier Public Key System. This threshold key includes the public key needed to encrypt a message (i.e. the n and g needed) and the public values needed to verify messages in the threshold scheme (i.e. the verifier v and the public verifier v_i for each decryption server).

The public key for the threshold variant is nothing more than the n and g as provided for in PaillierKey and the following additional public variables:

• l is the total number of decryption servers
• w is the threshold minimum number of decryption servers needed to decrypt a message; w must be less than or equal to half of l
• v is a number used to verify actions of the decryption servers. This value v generates the cyclic group of squares in Z^*_n^s+1
• v_i is a verification key unique to each decryption server i. The key v_i should be equal to v^Δs_i where Δ=l! (i.e. Δ is the factorial of the number of decryption servers).

The set of verification keys {v_i} is generated by the key generator and passed as an argument to this class, as well as all the above mentioned variables.

The public information contained in this key is sufficient to completely decrypt a ciphertext c, given the k≥w partial decryptions c₁,...,c_k.

NOTE: This is for the implementation where s=1.

Author:

James Garrity, Sean Hall

See Also:

PaillierThreshold, Serialized Form

Field Summary

private java.math.BigInteger	combineSharesConstant The cached value of (4Δ2)-1 mod ns
protected java.math.BigInteger	delta Δ=L!; this is used often in decryption algorithms.
protected int	l Number of decryption servers L.
private static long	serialVersionUID This Serial ID
protected java.math.BigInteger	v Generates a cyclic group of squares in Z*n2.
protected java.math.BigInteger[]	vi Verification key for each of the l decryption servers.
protected int	w The minimum of decryption servers needed to make a correct decryption.

Fields inherited from class paillierp.key.PaillierKey

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

Constructor Summary

PaillierThresholdKey(java.math.BigInteger n, int l, java.math.BigInteger combineSharesConstant, int w, java.math.BigInteger v, java.math.BigInteger[] viarray, long seed)
Creates a new public 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.

PaillierThresholdKey(java.math.BigInteger n, int l, int w, java.math.BigInteger v, java.math.BigInteger[] viarray, long seed)
Creates a new public 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.

PaillierThresholdKey(byte[] b, long seed)
Creates a new public threshold key using a byte encoding of a key.

Method Summary

java.math.BigInteger	getCombineSharesConstant() Returns a cached value of (4*Δ)-1 mod n.
java.math.BigInteger	getDelta() Returns the cached value Δ=l! where l is the number of decryption servers.
int	getL() Returns the number of decryption servers.
PaillierThresholdKey	getThresholdKey() The public key that may be used to encrypt data for private Paillier keys.
java.math.BigInteger	getV() Returns the public verification value.
java.math.BigInteger[]	getVi() Returns the verification keys for each decryption server.
int	getW() Returns the threshold number of decryption servers needed to successfully decrypt any ciphertext created by this key.
byte[]	toByteArray() Encodes this key into a byte array.

Methods inherited from class paillierp.key.PaillierKey

canEncrypt, 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

v

protected java.math.BigInteger v

Generates a cyclic group of squares in Z^*_n².

vi

protected java.math.BigInteger[] vi

Verification key for each of the l decryption servers. In essence, v_i=v^Δs_i.

l

protected int l

Number of decryption servers L.

delta

protected java.math.BigInteger delta

Δ=L!; this is used often in decryption algorithms.

w

protected int w

The minimum of decryption servers needed to make a correct decryption.

combineSharesConstant

private java.math.BigInteger combineSharesConstant

The cached value of (4Δ²)^-1 mod n^s

Constructor Detail

PaillierThresholdKey

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

Creates a new public 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.

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.

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

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

PaillierThresholdKey

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

Creates a new public 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.

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^s

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

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

PaillierThresholdKey

public PaillierThresholdKey(byte[] b,
                            long seed)

Creates a new public threshold 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

getThresholdKey

public PaillierThresholdKey getThresholdKey()

The public key that may be used to encrypt data for private Paillier keys. This includes the public values of v and {v_i} and l and w

Returns:

The Paillier public key corresponding to this key with with the public verification values.

getV

public java.math.BigInteger getV()

Returns the public verification value.

Returns:

verification value which generates the cyclic group of squares in Z^*_n²

getVi

public java.math.BigInteger[] getVi()

Returns the verification keys for each decryption server. Used for verification proofs.

Returns:

verification keys for each of the l decryption servers

getL

public int getL()

Returns the number of decryption servers.

Returns:

the number of decryption servers

getDelta

public java.math.BigInteger getDelta()

Returns the cached value Δ=l! where l is the number of decryption servers. This is frequently used for decryption.

Returns:

the value l!

getW

public int getW()

Returns the threshold number of decryption servers needed to successfully decrypt any ciphertext created by this key.

Returns:

the minimum number of decryption servers needed to make a correct decryption

getCombineSharesConstant

public java.math.BigInteger getCombineSharesConstant()

Returns a cached value of (4*Δ)^-1 mod n. This value is heavily used for decryption.

Returns:

the inverse of (4Δ) in Z_n

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, and vi 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 PaillierKey

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:

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