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Nilsimsa similarity hash - C#
Raw
README
Nilsimsa [1] is a similarity hash which is used as an anti-spam focused locality-sensitive hashing method [here]. This produces a score from 0 (dissimilar objects) to 128 (identical or very similar objects).
https://asecuritysite.com/hashsim/nil
Nilsima was created Damiani et al. in order to detect spam emails http://spdp.di.unimi.it/papers/pdcs04.pdf
It uses a 5-byte fixed-size sliding window that analyses the input on a byte-by-byte and produces trigrams of possible combinations of the input characters.
The trigrams map into a 256-bit array (known as the accumulator) to create the hash, and every time a given position is accessed, its value is incremented. At the end of the processing, if the values are above a certain threshold, the value is set to a 1, else it will be zero. This produces a 32-byte digest
To compare two hashes, the method checks the number of identical bits red to the the same position. This produces a score from 0 (dissimilar objects) to 128 (identical or very similar objects).
Raw
Nilsimsa.cs
using System;
using System.Text;
public class Nilsimsa
{
public const int DigestSize = 32;
// Internal state
private int _count;
private readonly int[] _acc;
private byte _c0, _c1, _c2, _c3;
// Predefined translation table (256 bytes)
private static readonly byte[] Tran = new byte[256]
{
0x02, 0xD6, 0x9E, 0x6F, 0xF9, 0x1D, 0x04, 0xAB,
0xD0, 0x22, 0x16, 0x1F, 0xD8, 0x73, 0xA1, 0xAC,
0x3B, 0x70, 0x62, 0x96, 0x1E, 0x6E, 0x8F, 0x39,
0x9D, 0x05, 0x14, 0x4A, 0xA6, 0xBE, 0xAE, 0x0E,
0xCF, 0xB9, 0x9C, 0x9A, 0xC7, 0x68, 0x13, 0xE1,
0x2D, 0xA4, 0xEB, 0x51, 0x8D, 0x64, 0x6B, 0x50,
0x23, 0x80, 0x03, 0x41, 0xEC, 0xBB, 0x71, 0xCC,
0x7A, 0x86, 0x7F, 0x98, 0xF2, 0x36, 0x5E, 0xEE,
0x8E, 0xCE, 0x4F, 0xB8, 0x32, 0xB6, 0x5F, 0x59,
0xDC, 0x1B, 0x31, 0x4C, 0x7B, 0xF0, 0x63, 0x01,
0x6C, 0xBA, 0x07, 0xE8, 0x12, 0x77, 0x49, 0x3C,
0xDA, 0x46, 0xFE, 0x2F, 0x79, 0x1C, 0x9B, 0x30,
0xE3, 0x00, 0x06, 0x7E, 0x2E, 0x0F, 0x38, 0x33,
0x21, 0xAD, 0xA5, 0x54, 0xCA, 0xA7, 0x29, 0xFC,
0x5A, 0x47, 0x69, 0x7D, 0xC5, 0x95, 0xB5, 0xF4,
0x0B, 0x90, 0xA3, 0x81, 0x6D, 0x25, 0x55, 0x35,
0xF5, 0x75, 0x74, 0x0A, 0x26, 0xBF, 0x19, 0x5C,
0x1A, 0xC6, 0xFF, 0x99, 0x5D, 0x84, 0xAA, 0x66,
0x3E, 0xAF, 0x78, 0xB3, 0x20, 0x43, 0xC1, 0xED,
0x24, 0xEA, 0xE6, 0x3F, 0x18, 0xF3, 0xA0, 0x42,
0x57, 0x08, 0x53, 0x60, 0xC3, 0xC0, 0x83, 0x40,
0x82, 0xD7, 0x09, 0xBD, 0x44, 0x2A, 0x67, 0xA8,
0x93, 0xE0, 0xC2, 0x56, 0x9F, 0xD9, 0xDD, 0x85,
0x15, 0xB4, 0x8A, 0x27, 0x28, 0x92, 0x76, 0xDE,
0xEF, 0xF8, 0xB2, 0xB7, 0xC9, 0x3D, 0x45, 0x94,
0x4B, 0x11, 0x0D, 0x65, 0xD5, 0x34, 0x8B, 0x91,
0x0C, 0xFA, 0x87, 0xE9, 0x7C, 0x5B, 0xB1, 0x4D,
0xE5, 0xD4, 0xCB, 0x10, 0xA2, 0x17, 0x89, 0xBC,
0xDB, 0xB0, 0xE2, 0x97, 0x88, 0x52, 0xF7, 0x48,
0xD3, 0x61, 0x2C, 0x3A, 0x2B, 0xD1, 0x8C, 0xFB,
0xF1, 0xCD, 0xE4, 0x6A, 0xE7, 0xA9, 0xFD, 0xC4,
0x37, 0xC8, 0xD2, 0xF6, 0xDF, 0x58, 0x72, 0x4E,
};
// Population count lookup table: popc[x] = number of 1's in x.
private static readonly byte[] Popc = new byte[256]
{
0x00, 0x01, 0x01, 0x02, 0x01, 0x02, 0x02, 0x03,
0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04,
0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
0x05, 0x06, 0x06, 0x07, 0x06, 0x07, 0x07, 0x08
};
public Nilsimsa()
{
_acc = new int[256];
Reset();
}
public void Reset()
{
_count = 0;
Array.Clear(_acc, 0, _acc.Length);
_c0 = _c1 = _c2 = _c3 = 0;
}
/// <summary>
/// Updates the hash with the given byte array.
/// </summary>
public void Update(byte[] data)
{
foreach (byte c4 in data)
{
_count++;
if (_count > 4)
{
byte old0 = _c0, old1 = _c1, old2 = _c2;
_acc[Tran53(c4, _c0, _c1, 0)]++;
_acc[Tran53(c4, _c0, _c2, 1)]++;
_acc[Tran53(c4, _c1, _c2, 2)]++;
_acc[Tran53(c4, _c0, _c3, 3)]++;
_acc[Tran53(c4, _c1, _c3, 4)]++;
_acc[Tran53(c4, _c2, _c3, 5)]++;
_acc[Tran53(_c3, _c0, c4, 6)]++;
_acc[Tran53(_c3, _c2, c4, 7)]++;
_c0 = c4;
_c1 = old0;
_c2 = old1;
_c3 = old2;
}
else if (_count > 3)
{
byte old0 = _c0, old1 = _c1, old2 = _c2;
_acc[Tran53(c4, _c0, _c1, 0)]++;
_acc[Tran53(c4, _c0, _c2, 1)]++;
_acc[Tran53(c4, _c1, _c2, 2)]++;
_c0 = c4;
_c1 = old0;
_c2 = old1;
_c3 = old2;
}
else if (_count > 2)
{
byte old0 = _c0, old1 = _c1;
_acc[Tran53(c4, _c0, _c1, 0)]++;
_c0 = c4;
_c1 = old0;
_c2 = old1;
}
else if (_count > 1)
{
byte old0 = _c0;
_c0 = c4;
_c1 = old0;
}
else
{
_c0 = c4;
}
}
}
/// <summary>
/// Updates the hash with the given string (UTF8 encoded).
/// </summary>
public void Update(string s)
{
if (!string.IsNullOrEmpty(s))
Update(Encoding.UTF8.GetBytes(s));
}
/// <summary>
/// Computes and returns the final 32-byte digest.
/// </summary>
public byte[] GetDigest()
{
int trigrams = 0;
if (_count == 3)
trigrams = 1;
else if (_count == 4)
trigrams = 4;
else if (_count > 4)
trigrams = 8 * _count - 28;
int threshold = trigrams / 256;
byte[] digest = new byte[DigestSize];
for (int i = 0; i < 256; i++)
{
if (_acc[i] > threshold)
{
int index = i >> 3;
digest[index] |= (byte)(1 << (i & 7));
}
}
Array.Reverse(digest);
return digest;
}
/// <summary>
/// Returns the hex string representation of the digest.
/// </summary>
public string HexDigest()
{
byte[] digest = GetDigest();
StringBuilder sb = new StringBuilder(digest.Length * 2);
foreach (byte b in digest)
sb.Append(b.ToString("x2"));
return sb.ToString();
}
/// <summary>
/// Computes the Nilsimsa digest for the given data.
/// </summary>
public static byte[] ComputeHash(byte[] data)
{
Nilsimsa n = new Nilsimsa();
n.Update(data);
return n.GetDigest();
}
/// <summary>
/// Computes the Nilsimsa digest for the given string.
/// </summary>
public static byte[] ComputeHash(string s)
{
return ComputeHash(Encoding.UTF8.GetBytes(s));
}
/// <summary>
/// Computes the hex string of the Nilsimsa digest.
/// </summary>
public static string HexSum(string s)
{
return BitConverter.ToString(ComputeHash(s)).Replace("-", "").ToLowerInvariant();
}
/// <summary>
/// Computes the bitwise similarity score between two 32-byte digests.
/// This score is defined as 128 minus the sum of the population counts
/// of the XOR differences.
/// </summary>
public static int BitsDiff(byte[] d1, byte[] d2)
{
if (d1.Length != DigestSize || d2.Length != DigestSize)
throw new ArgumentException("Digests must be 32 bytes long.");
int bits = 0;
for (int i = 0; i < DigestSize; i++)
{
bits += Popc[d1[i] ^ d2[i]];
}
return 128 - bits;
}
/// <summary>
/// The tran53 transformation function.
/// </summary>
private static byte Tran53(byte a, byte b, byte c, int n)
{
int first = Tran[(a + n) & 0xFF];
int second = Tran[b] * (n + n + 1);
int third = Tran[(c ^ Tran[n]) & 0xFF];
return (byte)(((first ^ second) + third) & 0xFF);
}
}
Raw
NilsimsaUnitTests.cs
using System;
using NUnit.Framework;
[TestFixture]
public class NilsimsaUnitTests
{
// Helper method: converts a hex string to a byte array.
public static byte[] HexToBytes(string hex)
{
int len = hex.Length;
byte[] bytes = new byte[len / 2];
for (int i = 0; i < len; i += 2)
{
bytes[i / 2] = Convert.ToByte(hex.Substring(i, 2), 16);
}
return bytes;
}
[Test]
public void TestEmptyAndAbcdefgh()
{
// Verify empty input produces 32 zero bytes.
string x = Nilsimsa.HexSum("");
Assert.That(x, Is.EqualTo("0000000000000000000000000000000000000000000000000000000000000000"));
// Verify "abcdefgh" produces expected digest.
x = Nilsimsa.HexSum("abcdefgh");
Assert.That(x, Is.EqualTo("14c8118000000000030800000004042004189020001308014088003280000078"));
}
[Test]
public void TestIncrementalUpdate()
{
// Create instance, update incrementally, and verify digest.
Nilsimsa n = new Nilsimsa();
n.Update("abcd");
n.Update("efgh");
string x = n.HexDigest();
Assert.That(x, Is.EqualTo("14c8118000000000030800000004042004189020001308014088003280000078"));
// Continue updating with "ijk" and verify updated digest.
n.Update("ijk");
x = n.HexDigest();
Assert.That(x, Is.EqualTo("14c811840010000c0328200108040630041890200217582d4098103280000078"));
}
[Test]
public void TestBitsDiff_AbcdefghijkVsAbcdefgh()
{
byte[] digest1 = Nilsimsa.ComputeHash("abcdefghijk");
byte[] digest2 = Nilsimsa.ComputeHash("abcdefgh");
int bitsDiff = Nilsimsa.BitsDiff(digest1, digest2);
Assert.That(bitsDiff, Is.EqualTo(109));
}
[Test]
public void TestBitsDiffHex()
{
string x1 = Nilsimsa.HexSum("abcdefghijk");
string x2 = Nilsimsa.HexSum("abcdefgh");
int bitsDiff = Nilsimsa.BitsDiff(HexToBytes(x1), HexToBytes(x2));
Assert.That(bitsDiff, Is.EqualTo(109));
}
[Test]
public void TestLongStrings_DiffNewSequenceMatcher()
{
string x1 = Nilsimsa.HexSum("return diff.NewSequenceMatcherFromFiles(srcPath, dstPath)");
string x2 = Nilsimsa.HexSum("return diff.NewSequenceMatcherFromFiles(dstPath, srcPath)");
Assert.That(x1, Is.EqualTo("8beb55d08d78fed441ede9301390b49b716a11af3962db70b24540338cb70035"));
Assert.That(x2, Is.EqualTo("8a5355d09968f8d451efeb309919949b73e211af7952c970f245403b8cb7a035"));
int bitsDiff = Nilsimsa.BitsDiff(HexToBytes(x1), HexToBytes(x2));
Assert.That(bitsDiff, Is.EqualTo(96));
}
[Test]
public void TestLongStrings_DiffXYZ()
{
string x1 = Nilsimsa.HexSum("return diff.XYZ");
string x2 = Nilsimsa.HexSum("return diff.NewSequenceMatcherFromFiles(dstPath, srcPath)");
Assert.That(x1, Is.EqualTo("84125570884ae840f042ea400400009a721891002011a071225247f7a5241018"));
Assert.That(x2, Is.EqualTo("8a5355d09968f8d451efeb309919949b73e211af7952c970f245403b8cb7a035"));
int bitsDiff = Nilsimsa.BitsDiff(HexToBytes(x1), HexToBytes(x2));
Assert.That(bitsDiff, Is.EqualTo(35));
}
[Test]
public void TestTabChangeCallback()
{
byte[] digest1 = Nilsimsa.ComputeHash("C.setTabChangeCallbackWrapper(h.ih())");
byte[] digest2 = Nilsimsa.ComputeHash("C.setTabChangeCallbackWrapper(ih)");
int bitsDiff = Nilsimsa.BitsDiff(digest1, digest2);
Assert.That(bitsDiff, Is.EqualTo(40));
}
[Test]
public void TestNilsimsa3()
{
string[] list = new string[]
{
"a",
"ab",
"abc",
"abcd",
"abcde",
"abcdef",
"abcdefg",
"abcdefgh",
"abcdefghi",
"abcdefghij",
"abcdefghijk",
"abcdefghijkl",
"abcdefghijklm",
"abcdefghijklmn",
"abcdefghijklmno",
"abcdefghijklmnop",
"abcdefghijklmnopq",
"abcdefghijklmnopqr",
"abcdefghijklmnopqrs",
"abcdefghijklmnopqrst",
"abcdefghijklmnopqrstu",
"abcdefghijklmnopqrstuv",
"abcdefghijklmnopqrstuvw",
"abcdefghijklmnopqrstuvwx",
"abcdefghijklmnopqrstuvwxy",
"abcdefghijklmnopqrstuvwxyz",
};
string[] results = new string[]
{
"0000000000000000000000000000000000000000000000000000000000000000",
"0000000000000000000000000000000000000000000000000000000000000000",
"0040000000000000000000000000000000000000000000000000000000000000",
"0440000000000000000000000000000000100000000000000008000000000000",
"0440008000000000000000000000000000100020001200000008001200000050",
"04c0018000000000000000000000000004188020001200000088001280000058",
"04c8118000000000030000000000002004188020001208004088001280000078",
"14c8118000000000030800000004042004189020001308014088003280000078",
"14c8118400000000030800010804043004189020021318094098003280000078",
"14c81184000000000308200108040430041890200217580d4098103280000078",
"14c811840010000c0328200108040630041890200217582d4098103280000078",
"14c811840010000ca328200108044630041890200a17586d4298103280000078",
"14ca11850010000ca328200188044630041898200a17586dc2d8103284000078",
"14ca11850030004ca3a8200188044630041898200a17586dc2d8107284000078",
"14ca11850032004ca3a8284188044730041898200a17586dc2d8107384000078",
"94ca11850432005ca3a828418804473004199c200a17586dc2d8107384004178",
"94ca11850433005ca3a82841880447341419be200a17586dc2d8107384004178",
"94ca11850433005ca3a82841a88457341419be201a17586dc6d8107384084178",
"94ca11850533005ca3b82841a88657361419be201a17586dc6d8107384084178",
"94ca11850533005ca3b82841aa8657371419be201a17587dc6d81077840c4178",
"94ca15850533005ca3b92841aa8657371419be201a17587dd6d81077844cc178",
"94ca15850533005ca3b92849aa8657371419be201a17587fd6d81077844cc978",
"94ca15850533045cabb92869aa8657371419bea01a17587fd6f81077c44cc978",
"94ca95850533045cabb93869aa8657371499beb01a17587fd6f8107fc44cc978",
"94ca95850733045cabb93869aa8657373499beb01a17587fd6f9107fc54cc978",
"94ca95850773045cabb93869ba8657373499beb81a17587fd6f9107fc54cc978",
};
byte[] compareResults = new byte[]
{
128,
127,
125,
120,
120,
120,
120,
120,
123,
122,
122,
121,
124,
123,
121,
123,
122,
124,
123,
123,
125,
122,
123,
124,
125,
};
byte[] step3CompareResults = new byte[]
{
116,
104,
109,
111,
111,
113,
114,
116,
};
Assert.That(list.Length, Is.EqualTo(results.Length), "Length mismatch between list and results");
for (int i = 0; i < list.Length; i++)
{
string hex = Nilsimsa.HexSum(list[i]);
Assert.That(hex, Is.EqualTo(results[i]), $"Mismatch at index {i}: {hex}");
}
Assert.That(list.Length, Is.EqualTo(compareResults.Length + 1), "Length mismatch between list and compareResults");
byte[] last = Nilsimsa.ComputeHash(list[0]);
for (int i = 1; i < list.Length; i++)
{
byte[] sum = Nilsimsa.ComputeHash(list[i]);
int bits = Nilsimsa.BitsDiff(sum, last);
Assert.That((byte)bits, Is.EqualTo(compareResults[i - 1]), $"Mismatch in BitsDiff at index {i}: {bits:x}");
last = sum;
}
int j = 0;
last = Nilsimsa.ComputeHash(list[0]);
for (int i = 4; i < list.Length; i += 3)
{
byte[] sum = Nilsimsa.ComputeHash(list[i]);
int bits = Nilsimsa.BitsDiff(sum, last);
Assert.That((byte)bits, Is.EqualTo(step3CompareResults[j]), $"Mismatch in step3 BitsDiff at index {i}: {bits:x}");
last = sum;
j++;
}
}
}
Raw
Program.cs
using System;
class Program
{
static void Main(string[] args)
{
string text1 = "this is the first string";
string text2 = "this is the second string";
string digest1 = Nilsimsa.HexSum(text1);
string digest2 = Nilsimsa.HexSum(text2);
byte[] hash1 = Nilsimsa.ComputeHash(text1);
byte[] hash2 = Nilsimsa.ComputeHash(text2);
int score = Nilsimsa.BitsDiff(hash1, hash2);
Console.WriteLine("Nilsimsa method");
Console.WriteLine($"String 1:\t{text1}");
Console.WriteLine($"String 2:\t{text2}");
Console.WriteLine("\n--------------");
Console.WriteLine($"String 1 digest: {digest1}");
Console.WriteLine($"String 2 digest: {digest2}");
Console.WriteLine($"Score:\t\t{score}\n");
Console.Read();
}
}
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