Reversing a hash function - c#

I have the following hash function, and I'm trying to get my way to reverse it, so that I can find the key from a hashed value.
uint Hash(string s)
{
uint result = 0;
for (int i = 0; i < s.Length; i++)
{
result = ((result << 5) + result) + s[i];
}
return result;
}
The code is in C# but I assume it is clear.
I am aware that for one hashed value, there can be more than one key, but my intent is not to find them all, just one that satisfies the hash function suffices.
EDIT :
The string that the function accepts is formed only from digits 0 to 9 and the chars '*' and '#' hence the Unhash function must respect this criteria too.
Any ideas? Thank you.

This should reverse the operations:
string Unhash(uint hash)
{
List<char> s = new List<char>();
while (hash != 0)
{
s.Add((char)(hash % 33));
hash /= 33;
}
s.Reverse();
return new string(s.ToArray());
}
This should return a string that gives the same hash as the original string, but it is very unlikely to be the exact same string.

Characters 0-9,*,# have ASCII values 48-57,42,35, or binary: 00110000 ... 00111001, 00101010, 00100011
First 5 bits of those values are different, and 6th bit is always 1. This means that you can deduce your last character in a loop by taking current hash:
uint lastChar = hash & 0x1F - ((hash >> 5) - 1) & 0x1F + 0x20;
(if this doesn't work, I don't know who wrote it)
Now roll back hash,
hash = (hash - lastChar) / 33;
and repeat the loop until hash becomes zero. I don't have C# on me, but I'm 70% confident that this should work with only minor changes.

Brute force should work if uint is 32 bits. Try at least 2^32 strings and one of them is likely to hash to the same value. Should only take a few minutes on a modern pc.
You have 12 possible characters, and 12^9 is about 2^32, so if you try 9 character strings you're likely to find your target hash. I'll do 10 character strings just to be safe.
(simple recursive implementation in C++, don't know C# that well)
#define NUM_VALID_CHARS 12
#define STRING_LENGTH 10
const char valid_chars[NUM_VALID_CHARS] = {'0', ..., '#' ,'*'};
void unhash(uint hash_value, char *string, int nchars) {
if (nchars == STRING_LENGTH) {
string[STRING_LENGTH] = 0;
if (Hash(string) == hash_value) { printf("%s\n", string); }
} else {
for (int i = 0; i < NUM_VALID_CHARS; i++) {
string[nchars] = valid_chars[i];
unhash(hash_value, string, nchars + 1);
}
}
}
Then call it with:
char string[STRING_LENGTH + 1];
unhash(hash_value, string, 0);

Hash functions are designed to be difficult or impossible to reverse, hence the name (visualize meat + potatoes being ground up)

I would start out by writing each step that result = ((result << 5) + result) + s[i]; does on a separate line. This will make solving a lot easier. Then all you have to do is the opposite of each line (in the opposite order too).

Related

SqlServer Checksum in C#

I'm using the chechsum function in sql server 2008 R2 and I would like to get the same int values in a C# app.
Is there any equivalent method in c# that returns the values like the sql checksum function?
Thanx
On SQL Server Forum, at this page, it's stated:
The built-in CHECKUM function in SQL Server is built on a series of 4 bit left rotational xor operations. See this post for more explanation.
I was able to port the BINARY_CHECKSUM to c# and it seems to be working... I'll be looking at the plain CHECKSUM later...
private int SQLBinaryChecksum(string text)
{
long sum = 0;
byte overflow;
for (int i = 0; i < text.Length; i++)
{
sum = (long)((16 * sum) ^ Convert.ToUInt32(text[i]));
overflow = (byte)(sum / 4294967296);
sum = sum - overflow * 4294967296;
sum = sum ^ overflow;
}
if (sum > 2147483647)
sum = sum - 4294967296;
else if (sum >= 32768 && sum <= 65535)
sum = sum - 65536;
else if (sum >= 128 && sum <= 255)
sum = sum - 256;
return (int)sum;
}
CHECKSUM docs don't disclose how it computes the hash. If you want a hash you can use in T-SQL and C#, pick from the algorithms supported in HashBytes
The T-SQL documentation does not specify what algorithm is used by checksum() outside of this:
CHECKSUM computes a hash value, called the checksum, over its list of arguments. The hash value
is intended for use in building hash indexes. If the arguments to CHECKSUM are columns, and an
index is built over the computed CHECKSUM value, the result is a hash index. This can be used for
equality searches over the columns.
It's unlikely to compute an MD5 hash, since its return value (the computed hash) is a 32-bit integer; an MD5 hash is 128 bits in length.
In case you need to do a checksum on a GUID, change dna2's answer to this:
private int SQLBinaryChecksum(byte[] text)
With a byte array, the value from SQL will match the value from C#. To test:
var a = Guid.Parse("DEAA5789-6B51-4EED-B370-36F347A0E8E4").ToByteArray();
Console.WriteLine(SQLBinaryChecksum(a));
vs SQL:
select BINARY_CHECKSUM(CONVERT(uniqueidentifier,'DEAA5789-6B51-4EED-B370-36F347A0E8E4'))
both answers will be -1897092103.
#Dan's implementation of BinaryChecksum can be greatly simplified down in c# down to
int SqlBinaryChecksum(string text)
{
uint accumulator = 0;
for (int i = 0; i < text.Length; i++)
{
var leftRotate4bit = (accumulator << 4) | (accumulator >> -4);
accumulator = leftRotate4bit ^ text[i];
}
return (int)accumulator;
}
This also makes it clearer what the algorithm is doing. For each character, a 4 bit circular shift then an xor with character's byte

Generate a bruteforce string given an offset?

Some years back when I was still a beginner at programming, I found some code online that could generate a bruteforce-code given an offset.
So for instance, if I did GetPassword(1) it would return "a", and if I did GetPassword(2) it would return "b" etc.
Every increment of the offset would provide the next possible combination of strings. A minimum and maximum length of the "password to guess" could also be provided.
Now I have no idea where this code is, or what the algorithm is called. I want to implement one myself, since I need it for URL-enshortening purposes. A user generates a URL that I want to look somewhat long these lines: http://fablelane.com/i/abc where "abc" is the code.
You can think of the output from GetPassword as a number in a different base. For example if GetPassword can output upper and lower case alphanumeric then it is in base 62 -> 26 letters + 26 letters + 10 digits.
GetPassword must convert from base 10 to base 62 in this case. You can use a look up array to find the output characters.
You can convert from one base to another by using an algorithm such as this:
Another stackoverflow post
This is base 26 encoding end decoding:
public static string Encode(int number){
number = Math.Abs(number);
StringBuilder converted = new StringBuilder();
// Repeatedly divide the number by 26 and convert the
// remainder into the appropriate letter.
do
{
int remainder = number % 26;
converted.Insert(0, (char)(remainder + 'a'));
number = (number - remainder) / 26;
} while (number > 0);
return converted.ToString();
}
public static int Decode(string number) {
if (number == null) throw new ArgumentNullException("number");
int s = 0;
for (int i = 0; i < number.Length; i++) {
s += (number[i] - 'a');
s = i == number.Length - 1 ? s : s * 26;
}
return s;
}

Calculating the number of bits in a Subnet Mask in C#

I have a task to complete in C#. I have a Subnet Mask: 255.255.128.0.
I need to find the number of bits in the Subnet Mask, which would be, in this case, 17.
However, I need to be able to do this in C# WITHOUT the use of the System.Net library (the system I am programming in does not have access to this library).
It seems like the process should be something like:
1) Split the Subnet Mask into Octets.
2) Convert the Octets to be binary.
3) Count the number of Ones in each Octet.
4) Output the total number of found Ones.
However, my C# is pretty poor. Does anyone have the C# knowledge to help?
Bit counting algorithm taken from:
http://www.necessaryandsufficient.net/2009/04/optimising-bit-counting-using-iterative-data-driven-development/
string mask = "255.255.128.0";
int totalBits = 0;
foreach (string octet in mask.Split('.'))
{
byte octetByte = byte.Parse(octet);
while (octetByte != 0)
{
totalBits += octetByte & 1; // logical AND on the LSB
octetByte >>= 1; // do a bitwise shift to the right to create a new LSB
}
}
Console.WriteLine(totalBits);
The most simple algorithm from the article was used. If performance is critical, you might want to read the article and use a more optimized solution from it.
string ip = "255.255.128.0";
string a = "";
ip.Split('.').ToList().ForEach(x => a += Convert.ToInt32(x, 2).ToString());
int ones_found = a.Replace("0", "").Length;
A complete sample:
public int CountBit(string mask)
{
int ones=0;
Array.ForEach(mask.Split('.'),(s)=>Array.ForEach(Convert.ToString(int.Parse(s),2).Where(c=>c=='1').ToArray(),(k)=>ones++));
return ones
}
You can convert a number to binary like this:
string ip = "255.255.128.0";
string[] tokens = ip.Split('.');
string result = "";
foreach (string token in tokens)
{
int tokenNum = int.Parse(token);
string octet = Convert.ToString(tokenNum, 2);
while (octet.Length < 8)
octet = octet + '0';
result += octet;
}
int mask = result.LastIndexOf('1') + 1;
The solution is to use a binary operation like
foreach(string octet in ipAddress.Split('.'))
{
int oct = int.Parse(octet);
while(oct !=0)
{
total += oct & 1; // {1}
oct >>=1; //{2}
}
}
The trick is that on line {1} the binary AND is in sence a multiplication so multiplicating 1x0=0, 1x1=1. So if we have some hypothetic number
0000101001 and multiply it by 1 (so in binary world we execute &), which is nothig else then 0000000001, we get
0000101001
0000000001
Most right digit is 1 in both numbers so making binary AND return 1, otherwise if ANY of the numbers minor digit will be 0, the result will be 0.
So here, on line total += oct & 1 we add to tolal either 1 or 0, based on that digi number.
On line {2}, instead we just shift the minor bit to right by, actually, deviding the number by 2, untill it becomes 0.
Easy.
EDIT
This is valid for intgere and for byte types, but do not use this technique on floating point numbers. By the way, it's pretty valuable solution for this question.

Number of unset bit left of most significant set bit?

Assuming the 64bit integer 0x000000000000FFFF which would be represented as
00000000 00000000 00000000 00000000
00000000 00000000 >11111111 11111111
How do I find the amount of unset bits to the left of the most significant set bit (the one marked with >) ?
In straight C (long long are 64 bit on my setup), taken from similar Java implementations: (updated after a little more reading on Hamming weight)
A little more explanation: The top part just sets all bit to the right of the most significant 1, and then negates it. (i.e. all the 0's to the 'left' of the most significant 1 are now 1's and everything else is 0).
Then I used a Hamming Weight implementation to count the bits.
unsigned long long i = 0x0000000000000000LLU;
i |= i >> 1;
i |= i >> 2;
i |= i >> 4;
i |= i >> 8;
i |= i >> 16;
i |= i >> 32;
// Highest bit in input and all lower bits are now set. Invert to set the bits to count.
i=~i;
i -= (i >> 1) & 0x5555555555555555LLU; // each 2 bits now contains a count
i = (i & 0x3333333333333333LLU) + ((i >> 2) & 0x3333333333333333LLU); // each 4 bits now contains a count
i = (i + (i >> 4)) & 0x0f0f0f0f0f0f0f0fLLU; // each 8 bits now contains a count
i *= 0x0101010101010101LLU; // add each byte to all the bytes above it
i >>= 56; // the number of bits
printf("Leading 0's = %lld\n", i);
I'd be curious to see how this was efficiency wise. Tested it with several values though and it seems to work.
Based on: http://www.hackersdelight.org/HDcode/nlz.c.txt
template<typename T> int clz(T v) {int n=sizeof(T)*8;int c=n;while (n){n>>=1;if (v>>n) c-=n,v>>=n;}return c-v;}
If you'd like a version that allows you to keep your lunch down, here you go:
int clz(uint64_t v) {
int n=64,c=64;
while (n) {
n>>=1;
if (v>>n) c-=n,v>>=n;
}
return c-v;
}
As you'll see, you can save cycles on this by careful analysis of the assembler, but the strategy here is not a terrible one. The while loop will operate Lg[64]=6 times; each time it will convert the problem into one of counting the number of leading bits on an integer of half the size.
The if statement inside the while loop asks the question: "can i represent this integer in half as many bits", or analogously, "if i cut this in half, have i lost it?". After the if() payload completes, our number will always be in the lowest n bits.
At the final stage, v is either 0 or 1, and this completes the calculation correctly.
If you are dealing with unsigned integers, you could do this:
#include <math.h>
int numunset(uint64_t number)
{
int nbits = sizeof(uint64_t)*8;
if(number == 0)
return nbits;
int first_set = floor(log2(number));
return nbits - first_set - 1;
}
I don't know how it will compare in performance to the loop and count methods that have already been offered because log2() could be expensive.
Edit:
This could cause some problems with high-valued integers since the log2() function is casting to double and some numerical issues may arise. You could use the log2l() function that works with long double. A better solution would be to use an integer log2() function as in this question.
// clear all bits except the lowest set bit
x &= -x;
// if x==0, add 0, otherwise add x - 1.
// This sets all bits below the one set above to 1.
x+= (-(x==0))&(x - 1);
return 64 - count_bits_set(x);
Where count_bits_set is the fastest version of counting bits you can find. See https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel for various bit counting techniques.
I'm not sure I understood the problem correctly. I think you have a 64bit value and want to find the number of leading zeros in it.
One way would be to find the most significant bit and simply subtract its position from 63 (assuming lowest bit is bit 0). You can find out the most significant bit by testing whether a bit is set from within a loop over all 64 bits.
Another way might be to use the (non-standard) __builtin_clz in gcc.
I agree with the binary search idea. However two points are important here:
The range of valid answers to your question is from 0 to 64 inclusive. In other words - there may be 65 different answers to the question. I think (almost sure) all who posted the "binary search" solution missed this point, hence they'll get wrong answer for either zero or a number with the MSB bit on.
If speed is critical - you may want to avoid the loop. There's an elegant way to achieve this using templates.
The following template stuff finds the MSB correctly of any unsigned type variable.
// helper
template <int bits, typename T>
bool IsBitReached(T x)
{
const T cmp = T(1) << (bits ? (bits-1) : 0);
return (x >= cmp);
}
template <int bits, typename T>
int FindMsbInternal(T x)
{
if (!bits)
return 0;
int ret;
if (IsBitReached<bits>(x))
{
ret = bits;
x >>= bits;
} else
ret = 0;
return ret + FindMsbInternal<bits/2, T>(x);
}
// Main routine
template <typename T>
int FindMsb(T x)
{
const int bits = sizeof(T) * 8;
if (IsBitReached<bits>(x))
return bits;
return FindMsbInternal<bits/2>(x);
}
Here you go, pretty trivial to update as you need for other sizes...
int bits_left(unsigned long long value)
{
static unsigned long long mask = 0x8000000000000000;
int c = 64;
// doh
if (value == 0)
return c;
// check byte by byte to see what has been set
if (value & 0xFF00000000000000)
c = 0;
else if (value & 0x00FF000000000000)
c = 8;
else if (value & 0x0000FF0000000000)
c = 16;
else if (value & 0x000000FF00000000)
c = 24;
else if (value & 0x00000000FF000000)
c = 32;
else if (value & 0x0000000000FF0000)
c = 40;
else if (value & 0x000000000000FF00)
c = 48;
else if (value & 0x00000000000000FF)
c = 56;
// skip
value <<= c;
while(!(value & mask))
{
value <<= 1;
c++;
}
return c;
}
Same idea as user470379's, but counting down ...
Assume all 64 bits are unset. While value is larger than 0 keep shifting the value right and decrementing number of unset bits:
/* untested */
int countunsetbits(uint64_t val) {
int x = 64;
while (val) { x--; val >>= 1; }
return x;
}
Try
int countBits(int value)
{
int result = sizeof(value) * CHAR_BITS; // should be 64
while(value != 0)
{
--result;
value = value >> 1; // Remove bottom bits until all 1 are gone.
}
return result;
}
Use log base 2 to get you the most significant digit which is 1.
log(2) = 1, meaning 0b10 -> 1
log(4) = 2, 5-7 => 2.xx, or 0b100 -> 2
log(8) = 3, 9-15 => 3.xx, 0b1000 -> 3
log(16) = 4 you get the idea
and so on...
The numbers in between become fractions of the log result. So typecasting the value to an int gives you the most significant digit.
Once you get this number, say b, the simple 64 - n will be the answer.
function get_pos_msd(int n){
return int(log2(n))
}
last_zero = 64 - get_pos_msd(n)

Are there any working implementations of the rolling hash function used in the Rabin-Karp string search algorithm?

I'm looking to use a rolling hash function so I can take hashes of n-grams of a very large string.
For example:
"stackoverflow", broken up into 5 grams would be:
"stack", "tacko", "ackov", "ckove",
"kover", "overf", "verfl", "erflo", "rflow"
This is ideal for a rolling hash function because after I calculate the first n-gram hash, the following ones are relatively cheap to calculate because I simply have to drop the first letter of the first hash and add the new last letter of the second hash.
I know that in general this hash function is generated as:
H = c1ak − 1 + c2ak − 2 + c3ak − 3 + ... + cka0 where a is a constant and c1,...,ck are the input characters.
If you follow this link on the Rabin-Karp string search algorithm , it states that "a" is usually some large prime.
I want my hashes to be stored in 32 bit integers, so how large of a prime should "a" be, such that I don't overflow my integer?
Does there exist an existing implementation of this hash function somewhere that I could already use?
Here is an implementation I created:
public class hash2
{
public int prime = 101;
public int hash(String text)
{
int hash = 0;
for(int i = 0; i < text.length(); i++)
{
char c = text.charAt(i);
hash += c * (int) (Math.pow(prime, text.length() - 1 - i));
}
return hash;
}
public int rollHash(int previousHash, String previousText, String currentText)
{
char firstChar = previousText.charAt(0);
char lastChar = currentText.charAt(currentText.length() - 1);
int firstCharHash = firstChar * (int) (Math.pow(prime, previousText.length() - 1));
int hash = (previousHash - firstCharHash) * prime + lastChar;
return hash;
}
public static void main(String[] args)
{
hash2 hashify = new hash2();
int firstHash = hashify.hash("mydog");
System.out.println(firstHash);
System.out.println(hashify.hash("ydogr"));
System.out.println(hashify.rollHash(firstHash, "mydog", "ydogr"));
}
}
I'm using 101 as my prime. Does it matter if my hashes will overflow? I think this is desirable but I'm not sure.
Does this seem like the right way to go about this?
i remember a slightly different implementation which seems to be from one of sedgewick's algorithms books (it also contains example code - try to look it up). here's a summary adjusted to 32 bit integers:
you use modulo arithmetic to prevent your integer from overflowing after each operation.
initially set:
c = text ("stackoverflow")
M = length of the "n-grams"
d = size of your alphabet (256)
q = a large prime so that (d+1)*q doesn't overflow (8355967 might be a good choice)
dM = dM-1 mod q
first calculate the hash value of the first n-gram:
h = 0
for i from 1 to M:
h = (h*d + c[i]) mod q
and for every following n-gram:
for i from 1 to lenght(c)-M:
// first subtract the oldest character
h = (h + d*q - c[i]*dM) mod q
// then add the next character
h = (h*d + c[i+M]) mod q
the reason why you have to add d*q before subtracting the oldest character is because you might run into negative values due to small values caused by the previous modulo operation.
errors included but i think you should get the idea. try to find one of sedgewick's algorithms books for details, less errors and a better description. :)
As i understand it's a function minimization for:
2^31 - sum (maxchar) * A^kx
where maxchar = 62 (for A-Za-z0-9). I've just calculated it by Excel (OO Calc, exactly) :) and a max A it found is 76, or 73, for a prime number.
Not sure what your aim is here, but if you are trying to improve performance, using math.pow will cost you far more than you save by calculating a rolling hash value.
I suggest you start by keeping to simple and efficient and you are very likely find it is fast enough.

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