I have this code


and I was expecting to get the same result, but somehow it is different.

My question is: how does Mathematica calculate hashing for strings? From common sense it should convert a string to integer and calculate it for some integer. If so, how does it convert the string to integer?


1 Answer 1


As of version 11.3.0, the documentation (and implementation) of Hash have been updated.

When given a string, the hash algorithm works on the bytes of that string's UTF-8 representation.

For an example, below hashing the string "a" is the same as hashing the single byte 97 (decimal):


(* "11.3.0 for Mac OS X x86 (64-bit) (March 5, 2018)" *)

Hash["a", "SHA"] === Hash[StringToByteArray["a"], "SHA"] === Hash[ByteArray[{97}], "SHA"]

(* True *)

It is also worth noting that unlike previous versions, ByteArray does have a special meaning and the hashing is performed directly on the underlying bytes.

That applies for all hash types except the one argument form Hash[e] which can also be specified as Hash[e, "Expression"].


Per @Kuba's request, I am adding some code that allows reproducing the results of string hashing as done in previous releases (back to version 9 anyway).

That is, of course, nothing like the actual implementation, just a mock-up intended to give the same hash values.

It has no error checking to speak of and probably is slower than it needs to be.

Clear[byteHash, stringHash];

byteHash[bytes_List, method_: "MD5"] := If[$VersionNumber >= 11.3
  Hash[ByteArray[bytes], method]
  Module[{tmp = CreateTemporary[], hash},
   BinaryWrite[tmp, bytes];
   hash = FileHash[tmp, method];

stringHash[str_?StringQ, method_: "MD5"] := 
 Module[{bytes, cc = ToCharacterCode[str]},
  bytes = Which[
    $VersionNumber >= 11.3, 
       ToCharacterCode[str, "UTF-8"],
    $VersionNumber >= 11.2 && Max[cc] >= 512, 
       ToCharacterCode[ToString[str, CharacterEncoding -> "ISO8859-1"]],
    $VersionNumber >= 9.0, 
       Mod[cc, 256],
  byteHash[bytes, method]
  • $\begingroup$ Thanks for both answers. can you add how was it working for pre V11.3? $\endgroup$
    – Kuba
    Mar 11, 2018 at 5:57
  • $\begingroup$ @Kuba Maybe you should undelete your answer, it sounds right to me. The string needs to be rewritten in ISO8859-1, so that for example the single character \[Alpha] would become 8 characters: \, [, A etc. $\endgroup$
    – ilian
    Mar 11, 2018 at 6:21
  • $\begingroup$ I will try to come back and review it later, I remember I deleted it because I was getting inconsistent results on Cloud vs Windows. I think I suspected that is only a matter of picking correct encoding here and there but somehow stopped investigating. $\endgroup$
    – Kuba
    Mar 11, 2018 at 6:25
  • 1
    $\begingroup$ It seems that Hash for ByteArray was overloaded too, otherwise I'd get the same result for Hash[ByteArray[{195, 153}], "SHA256"] in V11.2 and V11.3, right? It is not the case. And due to that internal issuess and a bug you mentioned I think I will not undelete my answer. It would help a lot if you could find some time to elaborate on history of Hash for strings/byte arrays etc, many people need to support their packages for older versions too. $\endgroup$
    – Kuba
    Mar 12, 2018 at 8:37
  • 1
    $\begingroup$ @Kuba Right, it's what I meant by "unlike previous versions, ByteArray ..." $\endgroup$
    – ilian
    Mar 12, 2018 at 14:51

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