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| <div class="subTitle">org.apache.pirk.encryption</div> |
| <h2 title="Class Paillier" class="title">Class Paillier</h2> |
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| <ul class="inheritance"> |
| <li>java.lang.Object</li> |
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| <pre>public final class <span class="typeNameLabel">Paillier</span> |
| extends java.lang.Object |
| implements java.io.Serializable</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> |
| </dl> |
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| <h3>Constructor Summary</h3> |
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| <th class="colOne" scope="col">Constructor and Description</th> |
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| <td class="colOne"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#Paillier-java.math.BigInteger-java.math.BigInteger-int-">Paillier</a></span>(java.math.BigInteger p, |
| java.math.BigInteger q, |
| int bitLength)</code> |
| <div class="block">Creates a Paillier algorithm with all parameters specified.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#Paillier-int-int-">Paillier</a></span>(int bitLength, |
| int certainty)</code> |
| <div class="block">Constructs a Paillier algorithm with generated keys.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#Paillier-int-int-int-">Paillier</a></span>(int bitLength, |
| int certainty, |
| int ensureBitSet)</code> |
| <div class="block">Constructs a Paillier algorithm with generated keys and optionally ensures a certain bit is set in the modulus.</div> |
| </td> |
| </tr> |
| </table> |
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| <h3>Method Summary</h3> |
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| <caption><span id="t0" class="activeTableTab"><span>All Methods</span><span class="tabEnd"> </span></span><span id="t2" class="tableTab"><span><a href="javascript:show(2);">Instance Methods</a></span><span class="tabEnd"> </span></span><span id="t4" class="tableTab"><span><a href="javascript:show(8);">Concrete Methods</a></span><span class="tabEnd"> </span></span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Method and Description</th> |
| </tr> |
| <tr id="i0" class="altColor"> |
| <td class="colFirst"><code>java.math.BigInteger</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#decrypt-java.math.BigInteger-">decrypt</a></span>(java.math.BigInteger c)</code> |
| <div class="block">Returns the plaintext message for a given ciphertext.</div> |
| </td> |
| </tr> |
| <tr id="i1" class="rowColor"> |
| <td class="colFirst"><code>java.math.BigInteger</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#encrypt-java.math.BigInteger-">encrypt</a></span>(java.math.BigInteger m)</code> |
| <div class="block">Returns the encrypted value of <code>m</code> using a generated random value.</div> |
| </td> |
| </tr> |
| <tr id="i2" class="altColor"> |
| <td class="colFirst"><code>java.math.BigInteger</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#encrypt-java.math.BigInteger-java.math.BigInteger-">encrypt</a></span>(java.math.BigInteger m, |
| java.math.BigInteger r)</code> |
| <div class="block">Returns the ciphertext of a message using the given random value.</div> |
| </td> |
| </tr> |
| <tr id="i3" class="rowColor"> |
| <td class="colFirst"><code>int</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#getBitLength--">getBitLength</a></span>()</code> |
| <div class="block">Returns the bit length of the modulus <code>N</code>.</div> |
| </td> |
| </tr> |
| <tr id="i4" class="altColor"> |
| <td class="colFirst"><code>java.math.BigInteger</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#getLambdaN--">getLambdaN</a></span>()</code> |
| <div class="block">Returns the value of Carmichael's function at <code>N</code>.</div> |
| </td> |
| </tr> |
| <tr id="i5" class="rowColor"> |
| <td class="colFirst"><code>java.math.BigInteger</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#getN--">getN</a></span>()</code> |
| <div class="block">Returns the RSA modulus value <code>N</code>.</div> |
| </td> |
| </tr> |
| <tr id="i6" class="altColor"> |
| <td class="colFirst"><code>java.math.BigInteger</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#getNSquared--">getNSquared</a></span>()</code> |
| <div class="block">Returns the value of <code>N</code><sup>2</sup>.</div> |
| </td> |
| </tr> |
| <tr id="i7" class="rowColor"> |
| <td class="colFirst"><code>java.math.BigInteger</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#getP--">getP</a></span>()</code> |
| <div class="block">Returns the value of the large prime <code>p</code>.</div> |
| </td> |
| </tr> |
| <tr id="i8" class="altColor"> |
| <td class="colFirst"><code>java.math.BigInteger</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/pirk/encryption/Paillier.html#getQ--">getQ</a></span>()</code> |
| <div class="block">Returns the value of the large prime <code>q</code>.</div> |
| </td> |
| </tr> |
| </table> |
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| </a> |
| <h3>Methods inherited from class java.lang.Object</h3> |
| <code>equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait</code></li> |
| </ul> |
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| <h4>Paillier</h4> |
| <pre>public Paillier(java.math.BigInteger p, |
| java.math.BigInteger q, |
| int bitLength)</pre> |
| <div class="block">Creates a Paillier algorithm with all parameters specified.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>p</code> - First large prime.</dd> |
| <dd><code>q</code> - Second large prime.</dd> |
| <dd><code>bitLength</code> - Bit length of the modulus <code>N</code>.</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code>java.lang.IllegalArgumentException</code> - If <code>p</code> or <code>q</code> do not satisfy primality constraints.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="Paillier-int-int-"> |
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| </a> |
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| <h4>Paillier</h4> |
| <pre>public Paillier(int bitLength, |
| int certainty)</pre> |
| <div class="block">Constructs a Paillier algorithm with generated keys. |
| <p> |
| The generated keys <code>p</code> and <code>q</code> will have half the given modulus bit length, and the given prime certainty. |
| <p> |
| The probability that the generated keys represent primes will exceed (1 - (1/2)<sup><code>certainty</code></sup>). The execution time of this constructor is |
| proportional to the value of this parameter.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>bitLength</code> - The bit length of the resulting modulus <code>N</code>.</dd> |
| <dd><code>certainty</code> - The probability that the new <code>p</code> and <code>q</code> represent prime numbers.</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code>java.lang.IllegalArgumentException</code> - If the <code>certainty</code> is less than the system allowed lower bound.</dd> |
| </dl> |
| </li> |
| </ul> |
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| </a> |
| <ul class="blockListLast"> |
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| <h4>Paillier</h4> |
| <pre>public Paillier(int bitLength, |
| int certainty, |
| int ensureBitSet)</pre> |
| <div class="block">Constructs a Paillier algorithm with generated keys and optionally ensures a certain bit is set in the modulus. |
| <p> |
| The generated keys <code>p</code> and <code>q</code> will have half the given modulus bit length, and the given prime certainty. |
| <p> |
| The probability that the generated keys represent primes will exceed (1 - (1/2)<sup><code>certainty</code></sup>). The execution time of this constructor is |
| proportional to the value of this parameter. |
| <p> |
| When ensureBitSet > -1 the value of bit "<code>ensureBitSet</code>" in modulus <code>N</code> will be set.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>bitLength</code> - The bit length of the resulting modulus <code>N</code>.</dd> |
| <dd><code>certainty</code> - The probability that the new <code>p</code> and <code>q</code> represent prime numbers.</dd> |
| <dd><code>ensureBitSet</code> - index of bit in <code>N</code> to ensure is set.</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code>java.lang.IllegalArgumentException</code> - If the <code>certainty</code> is less than the system allowed lower bound, or the index of <code>ensureBitSet</code> is greater than the <code>bitLength</code>.</dd> |
| </dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| <!-- ============ METHOD DETAIL ========== --> |
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| <a name="getP--"> |
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| </a> |
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| <h4>getP</h4> |
| <pre>public java.math.BigInteger getP()</pre> |
| <div class="block">Returns the value of the large prime <code>p</code>.</div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>p.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="getQ--"> |
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| </a> |
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| <h4>getQ</h4> |
| <pre>public java.math.BigInteger getQ()</pre> |
| <div class="block">Returns the value of the large prime <code>q</code>.</div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>q.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="getN--"> |
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| </a> |
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| <h4>getN</h4> |
| <pre>public java.math.BigInteger getN()</pre> |
| <div class="block">Returns the RSA modulus value <code>N</code>.</div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>N, the product of <code>p</code> and <code>q</code>.</dd> |
| </dl> |
| </li> |
| </ul> |
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| <h4>getNSquared</h4> |
| <pre>public java.math.BigInteger getNSquared()</pre> |
| <div class="block">Returns the value of <code>N</code><sup>2</sup>.</div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>N squared.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="getLambdaN--"> |
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| </a> |
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| <h4>getLambdaN</h4> |
| <pre>public java.math.BigInteger getLambdaN()</pre> |
| <div class="block">Returns the value of Carmichael's function at <code>N</code>. |
| <p> |
| The Carmichael function of <code>N</code> is the least common multiple of <code>p-1</code> and <code>q-1</code>,</div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>Carmichael's function at <code>N</code>.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="getBitLength--"> |
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| </a> |
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| <h4>getBitLength</h4> |
| <pre>public int getBitLength()</pre> |
| <div class="block">Returns the bit length of the modulus <code>N</code>.</div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>the bit length, as an integer.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="encrypt-java.math.BigInteger-"> |
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| </a> |
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| <h4>encrypt</h4> |
| <pre>public java.math.BigInteger encrypt(java.math.BigInteger m) |
| throws <a href="../../../../org/apache/pirk/utils/PIRException.html" title="class in org.apache.pirk.utils">PIRException</a></pre> |
| <div class="block">Returns the encrypted value of <code>m</code> using a generated random value.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>m</code> - the value to be encrypted.</dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>the encrypted value</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code><a href="../../../../org/apache/pirk/utils/PIRException.html" title="class in org.apache.pirk.utils">PIRException</a></code> - If <code>m</code> is not less than @{code N}.</dd> |
| </dl> |
| </li> |
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| <a name="encrypt-java.math.BigInteger-java.math.BigInteger-"> |
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| </a> |
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| <h4>encrypt</h4> |
| <pre>public java.math.BigInteger encrypt(java.math.BigInteger m, |
| java.math.BigInteger r) |
| throws <a href="../../../../org/apache/pirk/utils/PIRException.html" title="class in org.apache.pirk.utils">PIRException</a></pre> |
| <div class="block">Returns the ciphertext of a message using the given random value.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>m</code> - the value to be encrypted.</dd> |
| <dd><code>r</code> - the random value to use in the Pailler encryption.</dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>the encrypted value.</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code><a href="../../../../org/apache/pirk/utils/PIRException.html" title="class in org.apache.pirk.utils">PIRException</a></code> - If <code>m</code> is not less than @{code N}.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="decrypt-java.math.BigInteger-"> |
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| </a> |
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| <h4>decrypt</h4> |
| <pre>public java.math.BigInteger decrypt(java.math.BigInteger c)</pre> |
| <div class="block">Returns the plaintext message for a given ciphertext.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>c</code> - an encrypted value.</dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>the corresponding plaintext value.</dd> |
| </dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </div> |
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