The ElGamal crypto scheme. More...

Inheritance diagram for frodo2.solutionSpaces.crypto.ElGamalScheme:

Classes
class	ElGamalPublicKeyShare
	A public key share. More...

Public Member Functions
	ElGamalScheme (Element params)
	Constructor.
AddableInteger	decrypt (ElGamalBigInteger initialCypherText, ElGamalBigInteger partialDecryption)
ElGamalBigInteger	encrypt (AddableInteger cleartext)
ElGamalBigInteger	encrypt (AddableInteger cleartext, AddableInteger bound)
ElGamalBigInteger	reencrypt (ElGamalBigInteger cyphertext)
ElGamalBigInteger	partialDecrypt (ElGamalBigInteger initialCypherText, ElGamalBigInteger partialDecryption)
void	addPublicKeyShare (ElGamalPublicKeyShare share)
ElGamalPublicKeyShare	newPublicKeyShare ()
String	toString ()
Public Member Functions inherited from frodo2.solutionSpaces.crypto.CryptoScheme< AddableInteger, ElGamalBigInteger, ElGamalScheme.ElGamalPublicKeyShare >
K	newPublicKeyShare ()
void	addPublicKeyShare (K share)
	Records another share of the public key.
E	encrypt (C cleartext)
	Encrypts a cleartext.
E	reencrypt (E cyphertext)
	Re-encrypts a cyphertext.
E	partialDecrypt (E initialCypherText, E partialDecryption)
	Partially decrypts a cyphertext.
C	decrypt (E initialCypherText, E partialDecryption)
	Decrypts a cyphertext.

Static Public Member Functions
static void	main (String[] args)
	Creates a safe prime and a generator for use with the ElGamal scheme.

Private Member Functions
BigInteger	randomBigInteger ()
boolean	isPowerOf2 (BigInteger nbr)
	Tests whether a number is a power of 2.

Static Private Member Functions
static BigInteger	getSafePrime (BigInteger r, BigInteger t)
	Return a safe prime number.
static void	getSafePrimeAndGenerator ()
	Generate a safe prime, its generator and print them out.
static ArrayList< BigInteger >	getFactors (BigInteger r, BigInteger t)
	Returns the list of prime factors of 2rt.
static BigInteger	getGenerator (ArrayList< BigInteger > factors, BigInteger prime, SecureRandom rand)
	Return a generator.

Private Attributes
final BigInteger	p
	Prime number.
final BigInteger	pMinus3
	p - 3
final int	nbrBitsOfPminus3
	The number of bits of p - 3.
final BigInteger	g
	Number such that gcd(g,p) = 1.
BigInteger	y
	The overall public key, as the product of all the (g^x mod p) shares.
BigInteger	x
	private key in [1, p-2]
final int	size
	The default size of the ElGamal vector.
final SecureRandom	rand
	Random generator.
final boolean	debug
	If true, does not actually perform encryption/decryption.

Static Private Attributes
static final long	serialVersionUID = -4409105662996332812L
	Used for serialization.
static int	certainty
	Parameter used to create P.
static int	minBitLength
	Parameter used to create P.

Detailed Description

The ElGamal crypto scheme.

Author: Eric Zbinden, Thomas Leaute

Constructor & Destructor Documentation

◆ ElGamalScheme()

frodo2.solutionSpaces.crypto.ElGamalScheme.ElGamalScheme ( Element params )

Constructor.

Parameters

params the publicly known parameters

References g, p, pMinus3, rand, and size.

Member Function Documentation

◆ addPublicKeyShare()

void frodo2.solutionSpaces.crypto.ElGamalScheme.addPublicKeyShare ( ElGamalPublicKeyShare share )

See also: CryptoScheme.addPublicKeyShare(CryptoScheme.PublicKeyShare)

References p, and frodo2.solutionSpaces.crypto.ElGamalScheme.ElGamalPublicKeyShare.y.

◆ decrypt()

AddableInteger frodo2.solutionSpaces.crypto.ElGamalScheme.decrypt	(	ElGamalBigInteger	initialCypherText,
		ElGamalBigInteger	partialDecryption )

See also: CryptoScheme.decrypt(java.io.Serializable, java.io.Serializable)

References debug, isPowerOf2(), p, frodo2.solutionSpaces.AddableInteger.PlusInfinity.PLUS_INF, frodo2.solutionSpaces.crypto.ElGamalBigInteger.vector, and x.

Referenced by frodo2.solutionSpaces.crypto.ElGamalSchemeTest.min(), and frodo2.solutionSpaces.crypto.ElGamalSchemeTest.randomDecryptOnce().

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◆ encrypt() [1/2]

ElGamalBigInteger frodo2.solutionSpaces.crypto.ElGamalScheme.encrypt ( AddableInteger cleartext )

See also: CryptoScheme.encrypt(java.io.Serializable)

Warning: THE OUTPUT IS NOT REALLY ENCRYPTED! One has to call reencrypt() to encrypt it.

Referenced by frodo2.solutionSpaces.crypto.ElGamalSchemeTest.min(), and frodo2.solutionSpaces.crypto.ElGamalSchemeTest.randomDecryptOnce().

◆ encrypt() [2/2]

ElGamalBigInteger frodo2.solutionSpaces.crypto.ElGamalScheme.encrypt	(	AddableInteger	cleartext,
		AddableInteger	bound )

See also: CryptoScheme.encrypt(java.io.Serializable, java.io.Serializable)

Note: bound + 1 = infinity

References frodo2.solutionSpaces.AddableInteger.intValue(), and frodo2.solutionSpaces.AddableInteger.PlusInfinity.PLUS_INF.

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◆ getFactors()

ArrayList< BigInteger > frodo2.solutionSpaces.crypto.ElGamalScheme.getFactors	(	BigInteger	r,
		BigInteger	t )

staticprivate

Returns the list of prime factors of 2rt.

Parameters

r	a large random number
t	a prime number

Returns: the list of factor of 2rt

Referenced by getSafePrimeAndGenerator().

◆ getGenerator()

BigInteger frodo2.solutionSpaces.crypto.ElGamalScheme.getGenerator	(	ArrayList< BigInteger >	factors,
		BigInteger	prime,
		SecureRandom	rand )

staticprivate

Return a generator.

Parameters

factors	the list of the factor of the safe prime minus one (2rt-1)
prime	a safe prime
rand	an instance of SecureRandom

Returns: a generator for this safe prime

References rand, size, and x.

Referenced by getSafePrimeAndGenerator().

◆ getSafePrime()

BigInteger frodo2.solutionSpaces.crypto.ElGamalScheme.getSafePrime	(	BigInteger	r,
		BigInteger	t )

staticprivate

Return a safe prime number.

Parameters

r	a large random number
t	a large prime number

Returns: a prime number in the form 2rt+1

Note: r might be modified in a way to find p

References certainty.

Referenced by getSafePrimeAndGenerator().

◆ getSafePrimeAndGenerator()

void frodo2.solutionSpaces.crypto.ElGamalScheme.getSafePrimeAndGenerator ( )

staticprivate

Generate a safe prime, its generator and print them out.

References certainty, frodo2.generator, getFactors(), getGenerator(), getSafePrime(), minBitLength, and rand.

Referenced by main().

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◆ isPowerOf2()

boolean frodo2.solutionSpaces.crypto.ElGamalScheme.isPowerOf2 ( BigInteger nbr )

private

Tests whether a number is a power of 2.

Parameters

nbr	the number to test

Returns: whether the input number is a power of 2

Referenced by decrypt().

◆ main()

void frodo2.solutionSpaces.crypto.ElGamalScheme.main ( String[] args )

static

Creates a safe prime and a generator for use with the ElGamal scheme.

Parameters

args	minimum bit length, and prime certainty

Note: This implementation is an improvement over the one by David Bishop, "Introduction to Cryptography with Java Applets"

References certainty, getSafePrimeAndGenerator(), and minBitLength.

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◆ newPublicKeyShare()

ElGamalPublicKeyShare frodo2.solutionSpaces.crypto.ElGamalScheme.newPublicKeyShare ( )

See also: CryptoScheme.newPublicKeyShare()

References g, p, and randomBigInteger().

Referenced by frodo2.solutionSpaces.crypto.ElGamalSchemeTest.init().

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◆ partialDecrypt()

ElGamalBigInteger frodo2.solutionSpaces.crypto.ElGamalScheme.partialDecrypt	(	ElGamalBigInteger	initialCypherText,
		ElGamalBigInteger	partialDecryption )