Modifier and Type	Class and Description
public static class	Primes.MROutput Used to return the output from the Enhanced Miller-Rabin Probabilistic Primality Test
public static class	Primes.STOutput Used to return the output from the Shawe-Taylor Random_Prime Routine

Modifier and Type	Field and Description
private static final BigInteger	ONE
public static final int	SMALL_FACTOR_LIMIT
private static final BigInteger	THREE
private static final BigInteger	TWO

Access	Constructor and Description
public	Primes()

Method Summary

Modifier and Type	Method and Description
private static void	checkCandidate(BigInteger n, String name)
public static Primes.MROutput	Returns: an `MROutput` instance that can be further queried for details. enhancedMRProbablePrimeTest(BigInteger the `BigInteger` instance to test for primality. candidate, SecureRandom the source of randomness to use to choose bases. random, int the number of randomly-chosen bases to perform the test for. iterations) FIPS 186-4 C.3.2 Enhanced Miller-Rabin Probabilistic Primality Test Run several iterations of the Miller-Rabin algorithm with randomly-chosen bases.
private static int	extract32(byte[] bs)
public static Primes.STOutput	Returns: an `STOutput` instance containing the requested prime. generateSTRandomPrime(Digest the `Digest` instance to use (as "Hash()"). Cannot be null. hash, int the length (in bits) of the prime to be generated. Must be at least 2. length, byte[] the seed to be used for the generation of the requested prime. Cannot be null or empty. inputSeed) FIPS 186-4 C.6 Shawe-Taylor Random_Prime Routine Construct a provable prime number using a hash function.
public static boolean	Returns: `true` if the candidate is found to have any small factors, `false` otherwise. hasAnySmallFactors(BigInteger the `BigInteger` instance to test for division by small factors. candidate) A fast check for small divisors, up to some implementation-specific limit.
private static void	hash(Digest d, byte[] input, byte[] output, int outPos)
private static BigInteger	hashGen(Digest d, byte[] seed, int count)
private static boolean	implHasAnySmallFactors(BigInteger x)
private static boolean	implMRProbablePrimeToBase(BigInteger w, BigInteger wSubOne, BigInteger m, int a, BigInteger b)
private static Primes.STOutput	implSTRandomPrime(Digest d, int length, byte[] primeSeed)
private static void	inc(byte[] seed, int c)
public static boolean	Returns: `false` if any witness to compositeness is found amongst the chosen bases (so `candidate` is definitely NOT prime), or else `true` (indicating primality with some probability dependent on the number of iterations that were performed). isMRProbablePrime(BigInteger the `BigInteger` instance to test for primality. candidate, SecureRandom the source of randomness to use to choose bases. random, int the number of randomly-chosen bases to perform the test for. iterations) FIPS 186-4 C.3.1 Miller-Rabin Probabilistic Primality Test Run several iterations of the Miller-Rabin algorithm with randomly-chosen bases.
public static boolean	Returns: `false` if the specified base is a witness to compositeness (so `candidate` is definitely NOT prime), or else `true`. isMRProbablePrimeToBase(BigInteger the `BigInteger` instance to test for primality. candidate, BigInteger the base value to use for this iteration. base) FIPS 186-4 C.3.1 Miller-Rabin Probabilistic Primality Test (to a fixed base).
private static boolean	isPrime32(long x)

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

ONE	back to summary
private static final BigInteger ONE

SMALL_FACTOR_LIMIT	back to summary
public static final int SMALL_FACTOR_LIMIT

THREE	back to summary
private static final BigInteger THREE

TWO	back to summary
private static final BigInteger TWO

Constructor Detail

Primes	back to summary
public Primes()

Method Detail

checkCandidate	back to summary
private static void checkCandidate(BigInteger n, String name)

enhancedMRProbablePrimeTest back to summary

enhancedMRProbablePrimeTest	back to summary
public static Primes.MROutput enhancedMRProbablePrimeTest(BigInteger candidate, SecureRandom random, int iterations) FIPS 186-4 C.3.2 Enhanced Miller-Rabin Probabilistic Primality Test Run several iterations of the Miller-Rabin algorithm with randomly-chosen bases. This is an alternative to `isMRProbablePrime(BigInteger, SecureRandom, int)` that provides more information about a composite candidate, which may be useful when generating or validating RSA moduli. Parameters candidate:BigInteger the `BigInteger` instance to test for primality. random:SecureRandom the source of randomness to use to choose bases. iterations:int the number of randomly-chosen bases to perform the test for. Returns:Primes.MROutput an `MROutput` instance that can be further queried for details.

public static Primes.MROutput enhancedMRProbablePrimeTest(BigInteger candidate, SecureRandom random, int iterations)

FIPS 186-4 C.3.2 Enhanced Miller-Rabin Probabilistic Primality Test Run several iterations of the Miller-Rabin algorithm with randomly-chosen bases. This is an alternative to isMRProbablePrime(BigInteger, SecureRandom, int) that provides more information about a composite candidate, which may be useful when generating or validating RSA moduli.

Parameters

candidate:BigInteger: the BigInteger instance to test for primality.
random:SecureRandom: the source of randomness to use to choose bases.
iterations:int: the number of randomly-chosen bases to perform the test for.

Returns:Primes.MROutput

an MROutput instance that can be further queried for details.

extract32	back to summary
private static int extract32(byte[] bs)

generateSTRandomPrime back to summary

generateSTRandomPrime	back to summary
public static Primes.STOutput generateSTRandomPrime(Digest hash, int length, byte[] inputSeed) FIPS 186-4 C.6 Shawe-Taylor Random_Prime Routine Construct a provable prime number using a hash function. Parameters hash:Digest the `Digest` instance to use (as "Hash()"). Cannot be null. length:int the length (in bits) of the prime to be generated. Must be at least 2. inputSeed:byte[] the seed to be used for the generation of the requested prime. Cannot be null or empty. Returns:Primes.STOutput an `STOutput` instance containing the requested prime.

public static Primes.STOutput generateSTRandomPrime(Digest hash, int length, byte[] inputSeed)

FIPS 186-4 C.6 Shawe-Taylor Random_Prime Routine Construct a provable prime number using a hash function.

Parameters

hash:Digest: the Digest instance to use (as "Hash()"). Cannot be null.
length:int: the length (in bits) of the prime to be generated. Must be at least 2.
inputSeed:byte[]: the seed to be used for the generation of the requested prime. Cannot be null or empty.

Returns:Primes.STOutput

an STOutput instance containing the requested prime.

hasAnySmallFactors back to summary

hasAnySmallFactors	back to summary
public static boolean hasAnySmallFactors(BigInteger candidate) A fast check for small divisors, up to some implementation-specific limit. Parameters candidate:BigInteger the `BigInteger` instance to test for division by small factors. Returns:boolean `true` if the candidate is found to have any small factors, `false` otherwise.

public static boolean hasAnySmallFactors(BigInteger candidate)

A fast check for small divisors, up to some implementation-specific limit.

Parameters

candidate:BigInteger: the BigInteger instance to test for division by small factors.

Returns:boolean

true if the candidate is found to have any small factors, false otherwise.

hash	back to summary
private static void hash(Digest d, byte[] input, byte[] output, int outPos)

hashGen	back to summary
private static BigInteger hashGen(Digest d, byte[] seed, int count)

implHasAnySmallFactors	back to summary
private static boolean implHasAnySmallFactors(BigInteger x)

implMRProbablePrimeToBase	back to summary
private static boolean implMRProbablePrimeToBase(BigInteger w, BigInteger wSubOne, BigInteger m, int a, BigInteger b)

implSTRandomPrime	back to summary
private static Primes.STOutput implSTRandomPrime(Digest d, int length, byte[] primeSeed)

inc	back to summary
private static void inc(byte[] seed, int c)

isMRProbablePrime back to summary

isMRProbablePrime	back to summary
public static boolean isMRProbablePrime(BigInteger candidate, SecureRandom random, int iterations) FIPS 186-4 C.3.1 Miller-Rabin Probabilistic Primality Test Run several iterations of the Miller-Rabin algorithm with randomly-chosen bases. Parameters candidate:BigInteger the `BigInteger` instance to test for primality. random:SecureRandom the source of randomness to use to choose bases. iterations:int the number of randomly-chosen bases to perform the test for. Returns:boolean `false` if any witness to compositeness is found amongst the chosen bases (so `candidate` is definitely NOT prime), or else `true` (indicating primality with some probability dependent on the number of iterations that were performed).

public static boolean isMRProbablePrime(BigInteger candidate, SecureRandom random, int iterations)

FIPS 186-4 C.3.1 Miller-Rabin Probabilistic Primality Test Run several iterations of the Miller-Rabin algorithm with randomly-chosen bases.

Parameters

candidate:BigInteger: the BigInteger instance to test for primality.
random:SecureRandom: the source of randomness to use to choose bases.
iterations:int: the number of randomly-chosen bases to perform the test for.

Returns:boolean

false if any witness to compositeness is found amongst the chosen bases (so candidate is definitely NOT prime), or else true (indicating primality with some probability dependent on the number of iterations that were performed).

isMRProbablePrimeToBase back to summary

isMRProbablePrimeToBase	back to summary
public static boolean isMRProbablePrimeToBase(BigInteger candidate, BigInteger base) FIPS 186-4 C.3.1 Miller-Rabin Probabilistic Primality Test (to a fixed base). Run a single iteration of the Miller-Rabin algorithm against the specified base. Parameters candidate:BigInteger the `BigInteger` instance to test for primality. base:BigInteger the base value to use for this iteration. Returns:boolean `false` if the specified base is a witness to compositeness (so `candidate` is definitely NOT prime), or else `true`.

public static boolean isMRProbablePrimeToBase(BigInteger candidate, BigInteger base)

FIPS 186-4 C.3.1 Miller-Rabin Probabilistic Primality Test (to a fixed base). Run a single iteration of the Miller-Rabin algorithm against the specified base.

Parameters

candidate:BigInteger: the BigInteger instance to test for primality.
base:BigInteger: the base value to use for this iteration.

Returns:boolean

false if the specified base is a witness to compositeness (so candidate is definitely NOT prime), or else true.

isPrime32	back to summary
private static boolean isPrime32(long x)

org.bouncycastle.math.internal back to summary

public Class Primes.MROutput

Class Inheritance

extends Object

java.lang.Object
org.bouncycastle.math.internal.Primes.MROutput

Used to return the output from the Enhanced Miller-Rabin Probabilistic Primality Test

Field Summary

Modifier and Type	Field and Description
private BigInteger	factor
private boolean	provablyComposite

Constructor Summary

Access	Constructor and Description
private	MROutput(boolean provablyComposite, BigInteger factor)

Method Summary

Modifier and Type	Method and Description
public BigInteger	getFactor()
public boolean	isNotPrimePower()
public boolean	isProvablyComposite()
private static Primes.MROutput	probablyPrime()
private static Primes.MROutput	provablyCompositeNotPrimePower()
private static Primes.MROutput	provablyCompositeWithFactor(BigInteger factor)

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

factor	back to summary
private BigInteger factor

provablyComposite	back to summary
private boolean provablyComposite

Constructor Detail

MROutput	back to summary
private MROutput(boolean provablyComposite, BigInteger factor)

Method Detail

getFactor	back to summary
public BigInteger getFactor()

isNotPrimePower	back to summary
public boolean isNotPrimePower()

isProvablyComposite	back to summary
public boolean isProvablyComposite()

probablyPrime	back to summary
private static Primes.MROutput probablyPrime()

provablyCompositeNotPrimePower	back to summary
private static Primes.MROutput provablyCompositeNotPrimePower()

provablyCompositeWithFactor	back to summary
private static Primes.MROutput provablyCompositeWithFactor(BigInteger factor)

org.bouncycastle.math.internal back to summary

public Class Primes.STOutput

Class Inheritance

extends Object

java.lang.Object
org.bouncycastle.math.internal.Primes.STOutput

Used to return the output from the Shawe-Taylor Random_Prime Routine

Field Summary

Modifier and Type	Field and Description
private BigInteger	prime
private int	primeGenCounter
private byte[]	primeSeed

Constructor Summary

Access	Constructor and Description
private	STOutput(BigInteger prime, byte[] primeSeed, int primeGenCounter)

Method Summary

Modifier and Type	Method and Description
public BigInteger	getPrime()
public int	getPrimeGenCounter()
public byte[]	getPrimeSeed()

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

prime	back to summary
private BigInteger prime

primeGenCounter	back to summary
private int primeGenCounter

primeSeed	back to summary
private byte[] primeSeed

Constructor Detail

STOutput	back to summary
private STOutput(BigInteger prime, byte[] primeSeed, int primeGenCounter)

Method Detail

getPrime	back to summary
public BigInteger getPrime()

getPrimeGenCounter	back to summary
public int getPrimeGenCounter()

getPrimeSeed	back to summary
public byte[] getPrimeSeed()

public abstract Class Primes

Nested and Inner Type Summary

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

public Class Primes.MROutput

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

public Class Primes.STOutput

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail