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http://git-wip-us.apache.org/repos/asf/incubator-pirk/blob/b467b0b4/target/apidocs/org/apache/pirk/encryption/ModPowAbstraction.html
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href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;base,
-      <a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;exponent,
-      <a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;modulus)</code>
-<div class="block">Performs modPow: (<code>base</code>^<code>exponent</code>) 
mod <code>modulus</code>
- 
- This method uses the values of <code>paillier.useGMPForModPow</code> and 
<code>paillier.GMPConstantTimeMode</code> as they were when the class was 
loaded to decide
- which implementation of modPow to invoke.</div>
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 title="class or interface in java.math">BigInteger</a>&nbsp;exponent,
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 title="class or interface in 
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 title="class or interface in java.lang">wait</a></code></li>
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-<pre>public static&nbsp;<a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;modPow(<a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;base,
-                                <a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;exponent,
-                                <a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;modulus)</pre>
-<div class="block">Performs modPow: (<code>base</code>^<code>exponent</code>) 
mod <code>modulus</code>
- 
- This method uses the values of <code>paillier.useGMPForModPow</code> and 
<code>paillier.GMPConstantTimeMode</code> as they were when the class was 
loaded to decide
- which implementation of modPow to invoke.
- 
- These values can be reloaded by invoking static method 
<code>ModPowAbstraction.reloadConfiguration()</code></div>
-<dl>
-<dt><span class="returnLabel">Returns:</span></dt>
-<dd>The result of modPow</dd>
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java.math">BigInteger</a>&nbsp;modPow(long&nbsp;base,
-                                <a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;exponent,
-                                <a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;modulus)</pre>
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http://git-wip-us.apache.org/repos/asf/incubator-pirk/blob/b467b0b4/target/apidocs/org/apache/pirk/encryption/Paillier.html
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-<div class="subTitle">org.apache.pirk.encryption</div>
-<h2 title="Class Paillier" class="title">Class Paillier</h2>
-</div>
-<div class="contentContainer">
-<ul class="inheritance">
-<li><a 
href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true";
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-extends <a 
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 title="class or interface in java.lang">Object</a>
-implements <a 
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 title="class or interface in java.io">Serializable</a></pre>
-<div class="block">Implementation of the Paillier cryptosystem
- <p>
- The algorithm is as follows:
- <p>
- Let N=pq, be a RSA modulus where p,q are large primes of roughly the same 
length
- <p>
- The plaintext space is the additive group Z/NZ and the ciphertext space is 
the multiplicative group (Z/N^2 Z)*.
- <p>
- Public key: N, Private key: The factorization of N=pq.
- <p>
- Let lambda(N) be the Carmichael function of N (the exponent of the 
multiplicative group of units modulo N):
- <p>
- lambda(N) = lcm(p-1,q-1) = (p-1)(q-1)/gcd(p-1,q-1)
- <p>
- Encryption E(m) for a message m is as follows:
- <p>
- - Given N and m
- <p>
- - Select a random value r in (Z/NZ)*
- <p>
- - E(m) = (1 + mN)r^N mod N^2
- <p>
- Decryption D(c) for a ciphertext c is as follows:
- <p>
- - Given N, its factorization N=pq, and ciphertext c
- <p>
- - Set w = lambda(N)^-1 mod N
- <p>
- - Set x = c^(lambda(N))mod N^2
- <p>
- - Set y = (x-1)/N
- <p>
- - D(c) = yw mod N
- <p>
- Ref: Paillier, Pascal. "Public-Key Cryptosystems Based on Composite Degree 
Residuosity Classes." EUROCRYPT'99.</div>
-<dl>
-<dt><span class="seeLabel">See Also:</span></dt>
-<dd><a 
href="../../../../serialized-form.html#org.apache.pirk.encryption.Paillier">Serialized
 Form</a></dd>
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href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;pInput,
-        <a 
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 title="class or interface in java.math">BigInteger</a>&nbsp;qInput,
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specified</div>
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-        int&nbsp;certainty)</code>
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and prime certainty value</div>
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org.apache.pirk.encryption">Paillier</a></code></td>
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-<td class="colFirst"><code><a 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a></code></td>
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href="../../../../org/apache/pirk/encryption/Paillier.html#decrypt-java.math.BigInteger-">decrypt</a></span>(<a
 
href="http://docs.oracle.com/javase/8/docs/api/java/math/BigInteger.html?is-external=true";
 title="class or interface in java.math">BigInteger</a>&nbsp;c)</code>
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 title="class or interface in java.math">BigInteger</a>&nbsp;m)</code>
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- <p>
- (1) Generate the primes according to Java's BigInteger prime generation 
methods, which satisfy ANSI X9.80
- <p>
- or
- <p>
- (2) Bolster Java BigInteger's prime generation to meet the requirements of 
NIST SP 800-56B ("Recommendation for Pair-Wise Key Establishment Schemes Using
- Integer Factorization Cryptography") and FIPS 186-4 ("Digital Signature 
Standard (DSS)") for key generation using probable primes.
- <p>
- Relevant page: SP 800-56B: p30 
http://csrc.nist.gov/publications/nistpubs/800-56B/sp800-56B.pdf#page=30 
Heading: 5.4 Prime Number Generators
- <p>
- Relevant pages FIPS 186-4: p50-p53, p55, p71: Sections B.3.1, B.3.3
- <p>
- http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf#page=61
- <p>
- http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf#page=80
- <p>
- Headings of most interest: Table C.2 "Minimum number of rounds of M-R testing 
when generating primes for use in RSA Digital Signatures" and "The primes p and
- q shall be selected with the following constraints"</div>
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-<td class="colFirst"><code>static <a 
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 title="class or interface in java.math">BigInteger</a>[]</code></td>
-<td class="colLast"><code><span class="memberNameLink"><a 
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-            int&nbsp;certainty,
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href="http://docs.oracle.com/javase/8/docs/api/java/util/Random.html?is-external=true";
 title="class or interface in java.util">Random</a>&nbsp;rnd)</code>
-<div class="block">This method returns a two-long array containing a viable 
RSA p and q meeting FIPS 186-4 and SP 800-56B</div>
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 title="class or interface in java.math">BigInteger</a></code></td>
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href="http://docs.oracle.com/javase/8/docs/api/java/util/Random.html?is-external=true";
 title="class or interface in java.util">Random</a>&nbsp;rnd,
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 title="class or interface in java.math">BigInteger</a>&nbsp;p)</code>
-<div class="block">Method to generate a second prime, q, in relation to a 
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href="http://docs.oracle.com/javase/8/docs/api/java/util/Random.html?is-external=true";
 title="class or interface in java.util">Random</a>&nbsp;rnd)</code>
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java.math">BigInteger</a>&nbsp;getSinglePrime(int&nbsp;bitLength,
-                                        int&nbsp;certainty,
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 title="class or interface in java.util">Random</a>&nbsp;rnd)</pre>
-<div class="block">Method to generate a single prime
- <p>
- Will optionally ensure that the prime meets the requirements in NIST SP 
800-56B and FIPS 186-4
- <p>
- NOTE: bitLength corresponds to the FIPS 186-4 nlen parameter</div>
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java.math">BigInteger</a>&nbsp;getSecondPrime(int&nbsp;bitLength,
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- <p>
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- <p>
- NOTE: bitLength corresponds to the FIPS 186-4 nlen parameter</div>
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java.math">BigInteger</a>[]&nbsp;getPrimePair(int&nbsp;bitLength,
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