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<!DOCTYPE html>
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<title>Marschall Hash 3 (MHA3)</title>
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<div class="container"><div class="page"><pre>VIATHINKSOFT/WEBFAN D. Marschall
SPECIFICATION No. 7 ViaThinkSoft
First Draft: 2018 4 September 2024
=== Marschall Hash 3 (MHA3) ===
Abstract
This document describes the hash algorithm MHA3.
Identification of this Document
Revision: 2024-09-04
State: Deprecated
Filename: viathinksoft-std-0007-mha3.txt
URN: urn:x-viathinksoft:std:0007:2024-09-04
OID: 1.3.6.1.4.1.37476.3.2.1.3
{ iso(1) identified-organization(3) dod(6) internet(1)
private(4) enterprise(1) 37476 specifications(3)
algorithm(2) hash(1) mha3(3) }
WEID: weid:pen:SX0-3-2-1-3-7
IETF/RFC: (None)
Attachments
Reference implementation in PHP:
<a href="https://github.com/danielmarschall/php_utils/blob/master/vts_crypt.inc.php">https://github.com/danielmarschall/php_utils/blob/master/</a>
<a href="https://github.com/danielmarschall/php_utils/blob/master/vts_crypt.inc.php">vts_crypt.inc.php</a>
Copyright Notice
Copyright (c) 2018-2024 ViaThinkSoft and the persons identified as
the document authors. All rights reserved.
Licensed under the terms of the Apache 2.0 License.
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Table of Contents
<a href="#section-1">1</a> Introduction . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-3">3</a>
<a href="#section-1.1">1.1</a> Terminology . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-3">3</a>
<a href="#section-2">2</a> Definition . . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-3">3</a>
<a href="#section-2.1">2.1</a> Example . . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3">3</a> Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3.1">3.1</a> Modular Crypt Format Notation . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3.2">3.2</a> Heterogenous Systems Notation . . . . . . . . . . . . . . . <a href="#page-5">5</a>
<a href="#section-4">4</a> Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-6">6</a>
<a href="#section-5">5</a> Reference implementation . . . . . . . . . . . . . . . . . . . <a href="#page-7">7</a>
<a href="#section-6">6</a> Security Considerations . . . . . . . . . . . . . . . . . . . . <a href="#page-8">8</a>
<a href="#section-6.1">6.1</a> Runtime complexity . . . . . . . . . . . . . . . . . . . . <a href="#page-8">8</a>
<a href="#section-7">7</a> RA Considerations . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-8">8</a>
<a href="#section-8">8</a> References . . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-9">9</a>
<a href="#section-6.1">6.1</a> Normative References . . . . . . . . . . . . . . . . . . . <a href="#page-9">9</a>
<a href="#section-6.2">6.2</a> Informative References . . . . . . . . . . . . . . . . . . <a href="#page-9">9</a>
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-9">9</a>
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-9">9</a>
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<h2><a class="selflink" id="section-1" href="#section-1">1</a> Introduction</h2>
MHA3 is a method to strengthen a weak hash function, e.g. in case
that the development environment or hardware does not allow using a
new implementation of a modern hash variant like SHA256 or SHA3.
MHA3 was designed with following goals:
1. It should be simple to implement
2. The memory usage should be low
3. The calculation time should be high, to avoid brute force; the
complexity can be defined by the number of iterations
4. The length of the hash should be variable, i.e. "Extendable-Output
Function" (XOF)
5. It should hardening each hash, crc32 as well as md5
6. If the base hash function is compromised, MHA3 would be still
safe.
<h3><a class="selflink" id="section-1.1" href="#section-1.1">1.1</a> Terminology</h3>
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in
<a href="https://datatracker.ietf.org/doc/html/bcp14">BCP 14</a> [<a href="https://datatracker.ietf.org/doc/html/rfc2119">RFC2119</a>] [<a href="https://datatracker.ietf.org/doc/html/rfc8174">RFC8174</a>] when, and only when, they appear in all
capitals, as shown here.
<h2><a class="selflink" id="section-2" href="#section-2">2</a> Definition</h2>
MHA3(C,L,I) := A(C,L,0) xor ... xor A(C,L,I-1)
with:
A(C,L,n) := B(C,n*L) & ... & B(C,n*L+(L-1))
B(C,n) := Q(H(C & (R^n)))
Symbols:
C: input data.
L: Desired length of the hash in bytes (L >= 1).
I: Number of iterations (I >= 1).
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& is concatenation.
H(s) is an existing hash function (unsalted).
Q(s) is the sum of all bytes mod 256 of the string s.
R is a constant value. We choose the single byte 0x01.
R^n are n repetitions (concatenations) of R.
<h3><a class="selflink" id="section-2.1" href="#section-2.1">2.1</a> Example</h3>
First step:
MHA3("test",3,2) = A("test",3,0) xor A("test",3,1)
A("test",3,0) = B("test",0) & B("test",1) & B("test",2)
A("test",3,1) = B("test",3) & B("test",4) & B("test",5)
B("test",0) = Q(H("test"))
B("test",1) = Q(H("test" & 0x01))
B("test",2) = Q(H("test" & 0x01 & 0x01))
B("test",3) = Q(H("test" & 0x01 & 0x01 & 0x01))
B("test",4) = Q(H("test" & 0x01 & 0x01 & 0x01 & 0x01))
B("test",5) = Q(H("test" & 0x01 & 0x01 & 0x01 & 0x01 & 0x01))
Second step:
MHA3("test",3,2) = (B("test",0) & B("test",1) & B("test",2)) xor
(B("test",3) & B("test",4) & B("test",5))
Third step:
MHA3("test",3,2) = (Q(H("test"&(R^0))) & Q(H("test"&(R^1))) &
Q(H("test"&(R^2)))) xor
(Q(H("test"&(R^3))) & Q(H("test"&(R^4))) &
Q(H("test"&(R^5))))
<h2><a class="selflink" id="section-3" href="#section-3">3</a> Notation</h2>
<h3><a class="selflink" id="section-3.1" href="#section-3.1">3.1</a> Modular Crypt Format Notation</h3>
Format of the MCF:
$<id>$<params>$<salt>$<hash>
<id> is 1.3.6.1.4.1.37476.3.2.1.1
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<params> is a=<algo>,i=<iterations>,l=<length>
where <algo> is any valid hash algorithm (name scheme of PHP
hash_algos() preferred), e.g.
- sha3-512
- sha3-384
- sha3-256
- sha3-224
- sha512
- sha512/256
- sha512/224
- sha384
- sha256
- sha224
- sha1
- md5
Not possible with MHA3 are these hashes (because they have a special
salt-handling and output their own crypt format):
- bcrypt [Standardized crypt identifier 2, 2a, 2x, 2y]
- argon2i [Crypt identifier argon2i, not standardized]
- argon2id [Crypt identifier argon2i, not standardized]
<iterations> are the iterations.
<length> are the length.
<salt> is always empty for MHA3.
Like most Crypt-hashes, <hash> is Radix64 coded without padding and
with alphabet
'./0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'.
<h3><a class="selflink" id="section-3.2" href="#section-3.2">3.2</a> Heterogenous Systems Notation</h3>
The "heterogenous systems notation" (HSN) is DEPRECATED in favor of
the modular crypt format notation!
<mha3-oid>$<base-hash>$<length>$<iterations>$<hash-base64>
- <mha3-oid> is the OID for a MHA3 algorithm in its dot-notation
without leading dot, which is 1.3.6.1.4.1.37476.3.2.1.3
This OID has ASN.1 Notation:
{ iso(1) identified-organization(3) dod(6) internet(1) private(4)
enterprise(1) 37476 specification(3) algorithm(2) hash(1) mha3(3) }
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- <base-hash> should be an OID which represents the base hash ("H")
algorithm used, in dot-notation.
The following table shows the OIDs which have been assigned for
exchange between heterogenous systems. If you want to use a different
hash algorithm or a derivate of it, please define your own OID (you
can use an UUID OID, get a free IANA PEN OID, or a free ViaThinkSoft
OID), but please do not use this arc, since only ViaThinkSoft may
maintain it.
--------------------------------------------------------------
Base algorithm OID proposal
--------------------------------------------------------------
Message Digest 4 (MD4) 1.3.6.1.4.1.37476.3.2.1.99.1
Message Digest 5 (MD5) 1.3.6.1.4.1.37476.3.2.1.99.2
RIPEMD-160 1.3.6.1.4.1.37476.3.2.1.99.3
Secure Hash Algorithm 1.3.6.1.4.1.37476.3.2.1.99.4
Secure Hash Algorithm 1 1.3.6.1.4.1.37476.3.2.1.99.5
Secure Hash Algorithm 2/224 1.3.6.1.4.1.37476.3.2.1.99.6.224
Secure Hash Algorithm 2/256 1.3.6.1.4.1.37476.3.2.1.99.6.256
Secure Hash Algorithm 2/384 1.3.6.1.4.1.37476.3.2.1.99.6.384
Secure Hash Algorithm 2/512 1.3.6.1.4.1.37476.3.2.1.99.6.512
Secure Hash Algorithm 3/224 1.3.6.1.4.1.37476.3.2.1.99.7.224
Secure Hash Algorithm 3/256 1.3.6.1.4.1.37476.3.2.1.99.7.256
Secure Hash Algorithm 3/384 1.3.6.1.4.1.37476.3.2.1.99.7.384
Secure Hash Algorithm 3/512 1.3.6.1.4.1.37476.3.2.1.99.7.512
--------------------------------------------------------------
- <length> is the length of the resulting hash in bytes, e.g. 500.
- <iterations> is the number of iterations, e.g. 16.
- <hash-base64> is the resulting hash, encoded in Base64.
<h2><a class="selflink" id="section-4" href="#section-4">4</a> Test Vectors</h2>
MHA3 - Base algo 'sha1', Input '', Length '16', Iterations 500
MCF: $1.3.6.1.4.1.37476.3.2.1.3$a=sha1,i=500,l=16$$YWyFPPG1f7D
hBv.I9m78zu
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$16
$500$aY+HRRI3h9FjDx0KBo9A/w==
Hex: 698f8745123787d1630f1d0a068f40ff
MHA3 - Base algo 'sha1', Input '', Length '32', Iterations 500
MCF: $1.3.6.1.4.1.37476.3.2.1.3$a=sha1,i=500,l=32$$/A89J91ZJhZ
BOB5ahi.SVily.e466dkslCi8b92eGA6
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$32
$500$1CABLB3bLjbDQD7cjk0UXkn+0g688fmunEkAdB4gIC8=
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Hex: d420012c1ddb2e36c3403edc8e4d145e49fed20ebcf1f9ae9c4900741
e20202f
MHA3 - Base algo 'sha1',
Input 'The quick brown fox jumps over the lazy dog',
Length '16', Iterations 500
MCF: $1.3.6.1.4.1.37476.3.2.1.3$a=sha1,i=500,l=16$$E183Xe/hsyN
CTxYVuPvC1u
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$16
$500$G3A5Zg1ju+PEVzaXwRxE3w==
Hex: 1b7039660d63bbe3c4573697c11c44df
MHA3 - Base algo 'sha1',
Input 'The quick brown fox jumps over the lazy dog',
Length '32', Iterations 500
MCF: $1.3.6.1.4.1.37476.3.2.1.3$a=sha1,i=500,l=32$$x6av.OpWEDf
bTdD6sprBQv4RGInHuhuJ0MFrmyYbela
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$32
$500$z8cx0QrYGFhdVfF8urtDSx6TIKpJwjwL2OHto+adgnc=
Hex: cfc731d10ad818585d55f17cbabb434b1e9320aa49c23c0bd8e1eda3e
69d8277
<h2><a class="selflink" id="section-5" href="#section-5">5</a> Reference implementation</h2>
// Implementation in PHP, with hex output
function bytesum_mod256($x) {
$res = 0;
for ($i=0; $i<strlen($x); $i++)
$res = ($res + ord($x[$i])) % 256;
return $res;
}
function mha3($content, $length, $iterations, $base_algo='sha1') {
assert($iterations>=1);
$out = array();
for ($l=0; $l<$length; $l++) {
$out[$l] = 0;
}
for ($i=0; $i<$iterations; $i++) {
for ($l=0; $l<$length; $l++) {
$n = $i*$length + $l;
$salt = str_repeat(chr(1), $n);
$out[$l] ^= bytesum_mod256(
hash($base_algo, $content.$salt, true));
}
}
return array_to_binarystring($out);
}
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// Framework for PHP, with MCF output:
// <a href="https://github.com/danielmarschall/php_utils/blob/master///">https://github.com/danielmarschall/php_utils/blob/master/</a>
<a href="https://github.com/danielmarschall/php_utils/blob/master///">//</a> vts_crypt.inc.php
include 'vts_crypt.inc.php';
$hash = vts_password_hash($data, PASSWORD_VTS_MHA3,
['algo'=>'sha1', 'length'=>32, 'iterations'=>500]);
assert(vts_password_verify($data, $hash));
<h2><a class="selflink" id="section-6" href="#section-6">6</a> Security Considerations</h2>
Hash values play a crucial role in various security contexts, such as
password verification. For detailed guidance on securely managing
hashes, please consult the relevant literature or documentation.
MHA3 has not been proved to be secure. Use it with caution.
<h3><a class="selflink" id="section-6.1" href="#section-6.1">6.1</a> Runtime complexity</h3>
The number of hash OPs is <iterations> times <length>.
<h2><a class="selflink" id="section-7" href="#section-7">7</a> RA Considerations</h2>
OID: 1.3.6.1.4.1.37476.3.2.1.3
WEID: weid:pen:SX0-3-2-1-3-7
ASN1: { iso(1) identified-organization(3) dod(6) internet(1)
private(4) enterprise(1) 37476 specifications(3)
algorithm(2) hash(1) mha3(3) }
IRI: /.../Specifications/Algorithm/Hash/MHA3
OID: 1.3.6.1.4.1.37476.3.2.1.99
ASN1: { iso(1) identified-organization(3) dod(6) internet(1)
private(4) enterprise(1) 37476 specifications(3) algorithm(2)
hash(1) foreign(99) }
IRI: /.../Specifications/Algorithm/Hash/Foreign
WEID: weid:pen:SX0-3-2-1-2R-2
Children:
+ md4(1), IRI MD4
+ md5(3), IRI MD5
+ ripemd160(3), IRI RIPEMD-160
+ sha0(4), IRI SHA0
+ sha1(5), IRI SHA1
+ sha2(6), IRI SHA2
+ ... <a href="#page-224">224</a>
+ ... <a href="#page-256">256</a>
+ ... <a href="#page-384">384</a>
+ ... <a href="#page-512">512</a>
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+ ... ... <a href="#page-224">224</a>
+ ... ... <a href="#page-256">256</a>
+ sha3(7), IRI SHA3
+ ... <a href="#page-224">224</a>
+ ... <a href="#page-256">256</a>
+ ... <a href="#page-384">384</a>
+ ... <a href="#page-512">512</a>
+ shake(8), IRI SHAKE
+ ... <a href="#page-128">128</a>
+ ... <a href="#page-256">256</a>
<h2><a class="selflink" id="section-8" href="#section-8">8</a> References</h2>
<h3><a class="selflink" id="section-6.1" href="#section-6.1">6.1</a> Normative References</h3>
[<a id="ref-RFC2119">RFC2119</a>] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", <a href="https://datatracker.ietf.org/doc/html/bcp14">BCP 14</a>, <a href="https://datatracker.ietf.org/doc/html/rfc2119">RFC 2119</a>,
DOI 10.17487/RFC2119, March 1997,
<<a href="https://www.rfc-editor.org/info/rfc2119">https://www.rfc-editor.org/info/rfc2119</a>>.
<h3><a class="selflink" id="section-6.2" href="#section-6.2">6.2</a> Informative References</h3>
None
Acknowledgements
I would like to thank Melanie Wehowski for her long time support in
OIDplus and WEID projects.
This document was written in Nroff Internet Draft Editor by 3xA
Security.
<a href="https://aaa-sec.com/nroffedit/">https://aaa-sec.com/nroffedit/</a>
<a href="https://misc.daniel-marschall.de/patches/nroffedit/">https://misc.daniel-marschall.de/patches/nroffedit/</a> ("year 2020"
patch)
Authors' Addresses
Daniel Marschall
Postfach 11 53
69243 Bammental
Germany
Email: [email protected]
URI: <a href="https://www.viathinksoft.com/">https://www.viathinksoft.com/</a>
Marschall [Page 9]
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