Exploring Hashing Functions
[UNFINISHED]
Author
Stephen Wolfram
Title
Exploring Hashing Functions
[UNFINISHED]
Description
A Simple Function
Category
Educational Materials
Keywords
URL
http://www.notebookarchive.org/2019-08-98zxexs/
DOI
https://notebookarchive.org/2019-08-98zxexs
Date Added
2019-08-20
Date Last Modified
2019-08-20
File Size
346.58 kilobytes
Supplements
Rights
Redistribution rights reserved
Download
Open in Wolfram Cloud
Exploring Hashing Functions
[UNFINISHED]
Exploring Hashing Functions
[UNFINISHED]
[UNFINISHED]
A Simple Function
A Simple Function
Here’s a very simple function to do hashing of text:
In[]:=
hash[s_]:=Mod[Total[Flatten[ToCharacterCode[s]]],150]
The function works by adding up the codes for each character, then reducing the result mod 150.
Here’s the hash for the word “today”:
In[]:=
hash["today"]
Out[]=
95
Here’s the hash for another word:
In[]:=
hash["grandmother"]
Out[]=
79
Here are 50 random dictionary words:
In[]:=
RandomWord[50]
Out[]=
{subsidiarity,bespoken,thoughtful,languorous,pharmacopoeia,zydeco,obligation,jaggedness,nakedness,deliriously,misconception,hoecake,costumier,unhorse,toweling,pocket,cherry,sauce,seeing,intuitionist,stroking,yawner,indifference,greet,bargaining,aural,moussaka,docility,hatch,meal,wold,unutterable,pertinently,sickle,morn,goldbricking,draper,plaid,endways,dreadful,sentient,metastatic,bouquet,largo,means,demystify,administration,preach,aviation,adulator}
Here are their hashes:
In[]:=
hash/@%
Out[]=
{108,105,48,53,19,54,14,1,56,5,53,120,87,22,123,46,53,79,35,131,131,62,50,85,142,83,118,115,70,115,138,145,14,35,144,63,38,72,13,89,124,21,23,83,82,90,10,27,109,110}
The hashes for words in the dictionary are quite uniformly distributed:
In[]:=
Histogram[hash/@WordList[]]
Out[]=
A Slightly More General Function
A Slightly More General Function
Here’s a hash function that allows a parameter for the modulus:
In[]:=
hash[s_,n_]:=Mod[Total[Flatten[ToCharacterCode[s]]],n]
Here are the distributions of hash values for different moduli:
In[]:=
Table[Labeled[Histogram[hash[#,n]&/@WordList[]],n],{n,10,150,10}]
Out[]=
,
,
,
,
,
,
,
,
,
,
,
,
,
,
 |
10 |
 |
20 |
30 |
 |
40 |
50 |
 |
60 |
 |
70 |
 |
80 |
 |
90 |
 |
100 |
 |
110 |
120 |
130 |
140 |
150 |
For moduli around 110 something very funky is happening.
This figures out what character code hashes to 11 modulo 50:
In[]:=
Reduce[Mod[x,50]11&&97≤x≤122,x,Integers]
Out[]=
x111
Here’s the corresponding character:
In[]:=
FromCharacterCode[111]
Out[]=
o
And, yes, this hashes to 11:
In[]:=
hash["o",50]
Out[]=
11
But so does a completely different string:
In[]:=
hash["den",50]
Out[]=
11
[[[ ??? ]]]
[[[ ??? ]]]
In[]:=
RandomWord[10]
Out[]=
{undomesticated,rusted,providentially,steward,autobiographic,ophthalmic,keg,shoddily,antiquary,barmaid}
In[]:=
hash[#,50]&/@%34
Out[]=
{47,13,26,12,39,15,11,14,40,20}
In[]:=
BinCounts[%37]
Out[]=
{0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1}
In[]:=
%39[[26]]
Out[]=
0
In[]:=
hash["fish",50]
Out[]=
26
In[]:=
TextSentences[WikipediaData["bitcoin"],1]
Out[]=
Bitcoin (₿) is a cryptocurrency, a form of electronic cash.
In[]:=
hash[WikipediaData["bitcoin"],100]
Out[]=
43
In[]:=
hash[First[%],100]
Out[]=
44
More Serious Hashing
More Serious Hashing
In[]:=
Hash["hello","SHA256"]
Out[]=
20329878786436204988385760252021328656300425018755239228739303522659023427620
In[]:=
Hash[WikipediaData["bitcoin"],"SHA256"]
Out[]=
59009805363197200580720809828768295434018317903332306513204017537855452133148
In[]:=
Hash[WikipediaData["bitcoin"],"SHA256"]
Out[]=
59009805363197200580720809828768295434018317903332306513204017537855452133148
WikipediaData
In[]:=
Hash[StringReplace[WikipediaData["bitcoin"],"the""not the"],"SHA256"]
Out[]=
22216615053474496929343158117820983771266872158750982665228970735087282046964
In[]:=
Hash[WikipediaData["tungsten"],"SHA256"]
Out[]=
39965620585436161073133933688087297219316118411081412757635592095323742945334
In[]:=
Hash[WikipediaData["tungsten"],"SHA256"]
Out[]=
39965620585436161073133933688087297219316118411081412757635592095323742945334
In[]:=
$Version
Out[]=
11.3.0 for Mac OS X x86 (64-bit) (March 7, 2018)
In[]:=
StringLength[WikipediaData["tungsten"]]
Out[]=
27187
In[]:=
CloudPublish[WikipediaData["tungsten"]]
Out[]=
In[]:=
SendMail["s.wolfram@wolfram.com",%]
Out[]=
Success
 | ✓ |
|
{"the","cat","in","the","hat"}
In[]:=
BlockchainBlockData[-1]
Out[]=
BlockHash000000000000000000126c3fce1e3d0a8e31e011c9419b9eeb0f81430113aca1,BlockNumber564503,TimeMined,ByteCount919414,Nonce1343131669,Version536870912,Confirmations0,PreviousBlockHash0000000000000000000506a688429f00da6c741cd748792d21a6a4858eed4eb2,MerkleRootb5444b321166deec95c6f7bc4900d757e702d9ac0808db7c921ec32f61111468,TransactionList{27d9147497f818a549e005658b08e00a8f168d0d00bc7b990af9b96ec0ef0647,8ecd9bf8c24b7590c970947be9fae256d6ced14e78738686242dcdfd8bd96717,9b3592d9a1b992fd596ec1eeac6dbdd6df52de75336fa8c80cc46fcc9159ed0e,7eaf334f9883dd8958035efe1e750bf2c2c3f67f9f4edc8644688aedb286ad1e,ed2a9d19afe4d89685e386b3b2857e9d66fb81b2cec01f5c1a5959891d6a9949,3859f85215fe234ef9ff1075fc26ed4beaba813cb1c2eac30ded5d7ae8509aaa,a3c01a6f0d037db4a28287f277d7867eb75c3d723cf59b2ce75fb2b691d91373,36417ff6cece65031c3c4827908079ad02cf8d31bc633eaca2635251053ebc7c,fad8944af5ebc594b42414e087562591bca18beee384b8778095d3cc4d4942d4,eebaeb9712630a319bf051e112a6ef9c97d604966f1b71a189a7fdea86b04d77,eb3be3a82964fc35f4b44b19c0e5081a5f81cce1b656d060a84c27813f2f27ed,4fc3dbf00685aca740fbd573f82a013cf5e6bc52a8209008a18eb453dfdfb4a1,1c2c6f76d7f58ae8ecbd232e7b000262c2015328028ee9e97a952d3180ac7e8f,efafa04612a56af03b77aaa4ed0635fa4c67fe54817de12ffd70dce3bbb1ef73,62d1411a864bee764c34facc3c65dc8a26a88d64f6a4496d3c827b8fcd33ddab,7c978a87065e83bcb4f1427032900aa4e9db2b5923ca1580d41a09462a613df4,e5a7333a6c8251041896386024d242440e36c762557f8eb9dab84f858527b7c2,d6c95aa33fb0965f9702e439caa335945c0cca9888f0e1caf5d1e14cedd7a892,81ddd01e9303c58d972cf20eccb3a0dd6543e6dcaf8bea9e6403bad193697bba,68a37e4afcba693b3ea1e2201988969ed929958eca52b407e2455140a6ef445b,2e1afef0baee961176e70343bcbe4629010bd7d1f5a3245f0df3290476f03a28,3a1d78a9444e998667a973d553595adfdf5fef5fa3c7740b915ac2ad966bccd7,bb911d355ec71637ff4e8be00d55722a123cc5bf952e6e9e1907ff7d4c37981b,79406edec914090d038d1aaf3df260fc30f08b431e1f6ad32c3c43ee339e0e58,7241f34b18871767c82592770823a4e891d7d12e94c48e9b4631bcde35adea43,db71320d5d8b814ab5428efb1176610e60c5f3bb7224dc95482c0880195dd6e1,34c2686aff7820e4da81e80e0a3b2d3c16a2d6efbd457a9a47eb18c6cab95cc5,5b60b8733868f5a9ba52f5da38c02db68ccf6a95f4cb6a04be193fb53eea1905,bf976a594c3b0a6287a4c57e5a3618792db3a1b020f86f903c67da1f15cf86d4,4173f4be6e6d7065f5a0ee1ab4b9eb4472475572fbb7389802a110959cee4388,4b862c40d5a8484e3b16dae5437a7c8dee046399b5ed6b138714316c409319eb,6bb9d14f129e12b670f54c4aadb46661b714762c03aba5fd2f6675c5c0840952,e879d70c8a5590fc615d3fe788f6ae4a4f5392258c0ce6c7e59ab4ea1b62486e,f94bc8c383b13f128e72c52dacf829a15bb989481655e4c07d2f7f64eea21a62,7e0046899bdf3d6faff0a7c9eb28570f6c324fe5c600310790aed62bf611927f,4b8206ff3ecf8236b0b20249db280227285736c04082e5b993fe7be1fdeab574,e4a81d2acd08b593fbbe42f17fa2e3165b6ab7399f54744214ea61e529351363,49887d6a10aa76ba64f2e2ffbd6626dae3699c9e8f6497d4e87d0257b4c0e77e,4e5bb60cc7bdeb9d73de47e9e3a4618355e75d6c49d66301e451b95a2c40a257,b03533e1a6c3ed2cccddbc57e043ae422f80524ee56a0ad6cc4283469041d6c2,bed284525f0e73112232fd66e4437baad10ee49f6f35e63fb2d763809739fdb3,47e63aac7f45482729648fa3e5ced48721184c97effb5642f3d1c2c7ce19b25e,a3d66fcf76debf28ae0a9f235a1593243f077e03af039e62ec28ac4e77726eb6,e4f561f7b0cff3900382f0ef815898a37cafc21c95082749a3eaec8d44d56d7b,273fa5f10b263a93882ab11bfd26397d1ca06c9ce3b31e7be74e47f0abc9ed1f,e0cb3990bf2fc3f87fcd688cf80387db40f322d60151b944bbc73f3f76b375a2,0504e4477330c25205bd5b76cd0150506d4f9390b2a1c2e6febc3c32df3a67e2,631082844c7bb03110ededeaa26ced176174fa82df3f2cdd073f42752f5e4500,fc9074b48fa5c8a6a807e3cafa7e31e5fba6e4cdc25df6f93a0bdba6294147eb,e87a43b9e89e19a0364e2b56ddce36068ccec1b8ae337262673fb75dce04926c,bf6562788f5cb11df0236e0a871d63d633c5b6dc3dc2629ca4ee1c941575f503,fa82c604e73e2c4d1ecac746a2591fcfdacd4a420727f7290cf74c19d4312210,184e933cfc4f0c8a4fe61a5213c132e34897f11cd145a11863b5c969791d8b1f,0dc127d01067262f9371e7dbae09a3641b213ec9df3f0ffbe1f4c8d26fb61a82,85d9a5bc09145e15a433d0a382f07197b717482d09d1381741217751c74e9314,5d765b9a00b10fd04a12152ad9865a0d5fa0ec85a9e4090f4ff49066776be61c,1fee49bb20006c5ae3d88ada2efdb2e97c8907101766256e3be426d8f868523b,a5b7f0f78183a9383c95839d8b3a805361ecb2cd2e113e8ae078504e600d715c,d71172882555aee793d5452bd779de88018e5d37f6379b267e22d98407193ea6,ec7f9e14a9a9cc0d8d155536819a87290a08dcf1464c2171f3cba25803ab12c3,8d52c6a9b2f5ce3a109dc3f9d648f0c8c3025beee2cb3d0b649d7928f86d6496,74b7cc482dca04fc852f1233a963bb9a28e14c71c43a850d7041921fc9e40ffe,1f18e57f3540cfbf0fb2c83e87f6f825884e8f398aa4b20e4605e3afa1221c9b,df6c6c35d132c76f91513d2805e58e28a06c24e1dfb6d534a07747a183af2b97,23d624e14dc6cc2d7772889c1d435cf94cf48c978d87e001624432eda2b77992,0a0df6106ebe66f45da698e4869074fef12a9f01d835923b0704a5486171edf5,eb3eabedb41c03828cd4676bedece14eefe3e9fa06a3f890edebaf93b5bc115f,b49619c72f564b54dc5565711bf92b6c9371e6f74ae50b962a52379ca2297c6f,fb831af6560eb0ca672450e5c9f6deed7db0c2b8ceca3860f884644bd3dfc070,b29704ad113193d28765ae533d2311136d46d414be4e3ca59ae5f4e8e6a8b2b8,f87782a4a8398dd6ae24cb9aea925977227b65a6a685e5586669471382d170eb,d3988bee97b8a728ab3084df4d4348f4514afe35298b22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Tungsten, or wolfram, is a chemical element with symbol W and atomic number 74. The name tungsten comes from the former Swedish name for the tungstate mineral scheelite, tung sten or "heavy stone". Tungsten is a rare metal found naturally on Earth almost exclusively combined with other elements in chemical compounds rather than alone. It was identified as a new element in 1781 and first isolated as a metal in 1783. Its important ores include wolframite and scheelite.The free element is remarkable for its robustness, especially the fact that it has the highest melting point of all the elements discovered, melting at 3422 °C (6192 °F, 3695 K). It also has the highest boiling point, at 5930 °C (10706 °F, 6203 K). Its density is 19.3 times that of water, comparable to that of uranium and gold, and much higher (about 1.7 times) than that of lead. Polycrystalline tungsten is an intrinsically brittle and hard material (under standard conditions, when uncombined), making it difficult to work. However, pure single-crystalline tungsten is more ductile and can be cut with a hard-steel hacksaw.Tungsten's many alloys have numerous applications, including incandescent light bulb filaments, X-ray tubes (as both the filament and target), electrodes in gas tungsten arc welding, superalloys, and radiation shielding. Tungsten's hardness and high density give it military applications in penetrating projectiles. Tungsten compounds are also often used as industrial catalysts.Tungsten is the only metal from the third transition series that is known to occur in biomolecules that are found in a few species of bacteria and archaea. It is the heaviest element known to be essential to any living organism. However, tungsten interferes with molybdenum and copper metabolism and is somewhat toxic to more familiar forms of animal life.== Characteristics ===== Physical properties ===In its raw form, tungsten is a hard steel-grey metal that is often brittle and hard to work. If made very pu
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Sun 24 Feb 2019 16:45:42GMT-5.
In[]:=
256/4
Out[]=
64
In[]:=
Table[Take[IntegerDigits[Hash[n,"SHA256"],16,64],3],{n,100}]
Out[]=
{{4,14,5},{8,7,9},{5,10,14},{9,11,14},{7,8,7},{10,8,1},{13,9,13},{14,15,3},{5,13,15},{0,7,10},{6,11,2},{14,10,14},{14,13,3},{11,11,5},{8,13,1},{8,6,4},{11,6,2},{1,4,11},{10,3,15},{2,14,15},{0,13,12},{9,4,12},{14,10,1},{9,12,7},{15,2,0},{13,15,3},{4,14,14},{1,0,7},{2,4,10},{10,9,7},{6,3,12},{6,9,4},{4,13,14},{7,0,9},{10,12,9},{5,8,3},{14,11,11},{6,6,10},{0,0,11},{14,8,1},{12,5,10},{15,0,7},{1,12,10},{6,2,14},{8,6,14},{0,11,6},{15,9,14},{12,10,9},{15,0,14},{8,8,11},{13,15,12},{12,12,5},{13,3,5},{6,9,7},{15,13,13},{2,6,13},{3,7,12},{7,2,7},{5,6,8},{0,13,5},{11,14,5},{11,13,14},{7,5,4},{10,12,10},{12,2,15},{13,14,12},{8,12,15},{6,12,0},{14,3,6},{1,15,0},{3,10,13},{4,6,11},{8,11,9},{6,15,0},{15,8,14},{9,5,14},{15,1,2},{12,8,14},{6,6,9},{1,4,11},{10,0,4},{14,9,9},{1,7,3},{14,2,0},{11,9,2},{8,7,13},{13,6,7},{3,7,2},{6,14,5},{15,8,2},{14,6,0},{2,12,1},{4,2,2},{10,3,0},{4,10,9},{8,15,8},{9,13,1},{10,8,8},{12,0,5},{4,8,13}}
In[]:=
16^3
Out[]=
4096
In[]:=
Position[Table[Take[IntegerDigits[Hash[n,"SHA256"],16,64],3],{n,5000}],{0,0,0}]
Out[]=
{{1238}}
In[]:=
Position[Table[Take[IntegerDigits[Hash[n,"SHA256"],16,64],3],{n,20000}],{0,0,0}]
Out[]=
{{1238},{9313},{9452},{9601}}
In[]:=
StringLength["0000000000000000000506a688429f00da6c741cd748792d21a6a4858eed4eb2"]
Out[]=
64
In[]:=
"0000000000000000000"//StringLength
Out[]=
19
In[]:=
16^19
Out[]=
75557863725914323419136
In[]:=
BlockchainBlockData[1]
Out[]=
BlockHash000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f,BlockNumber1,TimeMined,ByteCount285,Nonce2083236893,Version1,Confirmations564502,PreviousBlockHash0000000000000000000000000000000000000000000000000000000000000000,MerkleRoot4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b,TransactionList{}
Sat 3 Jan 2009 13:15:05GMT-5.
In[]:=
BlockchainTransactionData["0c7661837b5c2d4c8ab608bf1f65402129ad36a45feda09abcfb6b59bbfc187f"]
Out[]=
TransactionID0c7661837b5c2d4c8ab608bf1f65402129ad36a45feda09abcfb6b59bbfc187f,ByteCount225,Confirmations2,TotalBitcoins,Fee,Time,BlockHash0000000000000000000506a688429f00da6c741cd748792d21a6a4858eed4eb2,InputsSourceTransaction9b8f0043adaac84efcce9e469fd2f61acb3d5b1b74c3cbc0a06ad37136170b4d,ScriptByteArrayByteArray
,SequenceNumber4294967295,Addresses{1JJiyVXnAXCMJDF7bSkmTre6WKoQtMkwE4},SourceConfirmations564501,OutputsAmount,ScriptByteArrayByteArray
,Addresses{1FERjQPhhLJTiNNuBSJBfCrNb1ShuZUZza},Amount,ScriptByteArrayByteArray
,DestinationTransaction50fe54ae826b474751729a9eafedfd184657780db88c6d8c9da8fa5dc7069214,Addresses{14C64JCFcSig3zf7UAQ5oc1CwFbwB49F7j}
฿
0.0146364678.
s
Sun 24 Feb 2019 16:45:42GMT-5.
|
฿
0.0001
|
฿
0.0145364
|
In[]:=
CurrencyConvert,"USDollars"
฿
0.014636380000000001`Out[]=
$
55.09In[]:=
CurrencyConvert,"USDollars"
฿
0.0001`Out[]=
$
0.38In[]:=
ByteArray
|
Out[]=
ByteArray
|
In[]:=
Normal[%]
Out[]=
{71,48,68,2,32,4,120,40,80,136,148,37,223,162,18,146,221,187,179,125,89,255,184,245,94,112,140,144,231,248,17,54,139,172,90,157,63,2,32,82,227,131,183,74,51,22,174,162,208,132,122,241,202,116,130,249,175,110,171,247,210,244,17,155,217,209,28,5,189,113,45,1,33,3,216,49,245,165,102,31,174,62,73,81,233,88,214,25,47,94,202,164,80,179,120,96,228,29,194,120,48,182,184,81,165,164}
Cite this as: Stephen Wolfram, "Exploring Hashing Functions
[UNFINISHED]" from the Notebook Archive (2019), https://notebookarchive.org/2019-08-98zxexs
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