VIATHINKSOFT/WEBFAN D. Marschall
SPECIFICATION No. 6 ViaThinkSoft
First Draft: 2014 4 September 2024
=== Marschall Hash 2 (MHA2) ===
Abstract
This document describes the hash algorithm MHA2.
Identification of this Document
Revision: 2024-09-04
State: Deprecated
Filename: viathinksoft-std-0006-mha2.txt
URN: urn:x-viathinksoft:std:0006:2024-09-04
OID: 1.3.6.1.4.1.37476.3.2.1.2
{ iso(1) identified-organization(3) dod(6) internet(1)
private(4) enterprise(1) 37476 specifications(3)
algorithm(2) hash(1) mha2(2) }
WEID: weid:pen:SX0-3-2-1-2-9
IETF/RFC: (None)
Attachments
Reference implementation in PHP:
https://github.com/danielmarschall/php_utils/blob/master/
vts_crypt.inc.php
Copyright Notice
Copyright (c) 2014-2024 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
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Modular Crypt Format Notation . . . . . . . . . . . . . . . 4
3.2 Heterogenous Systems Notation . . . . . . . . . . . . . . . 5
4 Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 6
5 Reference implementation . . . . . . . . . . . . . . . . . . . 8
6 Security Considerations . . . . . . . . . . . . . . . . . . . . 8
6.1 Runtime complexity . . . . . . . . . . . . . . . . . . . . 10
7 RA Considerations . . . . . . . . . . . . . . . . . . . . . . . 11
8 References . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.1 Normative References . . . . . . . . . . . . . . . . . . . 11
6.2 Informative References . . . . . . . . . . . . . . . . . . 12
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . 12
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 12
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1 Introduction
MHA2 is a method to strengten 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 SHA3.1.1 Terminology
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 BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.2 Definition
MHA2(i,s,x) := A(i,s,x) xor B(i,s,x) xor C(i,s,x) with: A(j,s,x) := j>=0: H(P & A(j-1, s, x) & x & s & Q) j=-1: '' B(j,s,x) := j<=0: H(Q & s & x & B(j-1, s, x) & P) j=-1: '' C(j,s,x) := H( (K&x&s)*(j+1) ) K := 0x24 & 0x12 & 0x19 & 0x87 P := 0x12 & 0x24 & 0x19 & 0x87 Q := 0x19 & 0x87 & 0x12 & 0x24 where: i is the number of iterations, i <= 0. j is a number <= -1 . s is the salt. x is the input data. 0xd is a single byte with the hexadecimal value d. H(z) is an existing hash function. All hash operations have a binary output; no string conversation is done. x*z are z repetitions (concatenations) of x. Marschall [Page 3]VTS/WF STD. 6 ViaThinkSoft MHA2 4 September 2024
& is concatenation.
2.1 Example
- MHA2(1, '', x) = H(P & H(P&x&Q) & x & Q) xor H(Q & x & H(Q&x&P) & P) xor H(K&x&s & K&x&s) - MHA2(1, s, x) = H(P & H(P&x&s&Q) & x & s & Q) xor H(Q & s & x & H(Q&s&x&P) & P) xor H(K&x&s & K&x&s)3 Notation
3.1 Modular Crypt Format Notation
Format of the MCF: $<id>$<params>$<salt>$<hash> <id> is 1.3.6.1.4.1.37476.3.2.1.1 <params> is a=<algo>,i=<iterations> 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 MHA2 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. Like most Crypt-hashes, <salt> and <hash> are Radix64 coded without padding and with alphabet './0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'. Marschall [Page 4]VTS/WF STD. 6 ViaThinkSoft MHA2 4 September 2024
3.2 Heterogenous Systems Notation
The "heterogenous systems notation" (HSN) is DEPRECATED in favor of the modular crypt format notation! <mha2-oid>$<base-hash>$<iterations>$<salt-base64>$<hash-base64> - <mha2-oid> is the OID for a MHA2 algorithm in its dot-notation without leading dot, which is 1.3.6.1.4.1.37476.3.2.1.2 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) mha2(2) } - <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 -------------------------------------------------------------- - <iterations> is the number of iterations, e.g. 1987. - <salt-base64> is the iterated salt used for MHA2, encoded in Base64. - <hash-base64> is the resulting hash, encoded in Base64. Marschall [Page 5]VTS/WF STD. 6 ViaThinkSoft MHA2 4 September 2024
4 Test Vectors
MHA2 - Base algo 'sha1', Input '', Salt '', Iterations 0 MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=0$$NKCUx/Vbzl1cuIdoIA WNBJapRpG HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$0$ $PMEWz1Xd/n3ewKfqKCYPDLcrTrI= Hex: 3cc116cf55ddfe7ddec0a7ea28260f0cb72b4eb2 MHA2 - Base algo 'sha1', Input '', Salt '', Iterations 1 MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=1$$PoioZBIxVWuqt0nym5 qyhAszLwC HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$1$ $RqkqbDKzXYwsv2p+o7s+jCu/NyE= Hex: 46a92a6c32b35d8c2cbf6a7ea3bb3e8c2bbf3721 MHA2 - Base algo 'sha1', Input '', Salt '', Iterations 2 MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=2$$1zU5hmBQ9/ZewYq43q rXd2D8QRK HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$2$ $3/W7joDSB1bgyas65stZf4FASTM= Hex: dff5bb8e80d20756e0c9ab3ae6cb597f81404933 MHA2 - Base algo 'sha1', Input '', Salt 'salt', Iterations 0 MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=0$a0Dqb8$zZjdOSIocsFG Qp/.hpoYQLOfiN6 HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$0$ c2FsdA==$/blfQUKqeuHISr10jrqaSNQhkP8= Hex: fdb95f4142aa7ae1c84abd748eba9a48d42190ff MHA2 - Base algo 'sha1', Input '', Salt 'salt', Iterations 1 MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=1$a0Dqb8$BkKmNoOvKEss 6ek6EyXArDX1Z.8 HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$1$ c2FsdA==$DmMoPqQxMGuu8gm8G+ZCtFZ3b0A= Hex: 0e63283ea431306baef209bc1be642b456776f40 MHA2 - Base algo 'sha1', Input '', Salt 'salt', Iterations 2 MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=2$a0Dqb8$8HauBcPn31A4 EuUKUf.vcbg1K/O HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$2$ c2FsdA==$AJcwDeRp53C6GwWMWh0xedi3M1Q= Hex: 0097300de469e770ba1b058c5a1d3179d8b73354 MHA2 - Base algo 'sha1', Input 'The quick brown fox jumps over the lazy dog', Salt '', Iterations 0 MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=0$$/oEBf.u/XEwY8r12lI Marschall [Page 6]VTS/WF STD. 6 ViaThinkSoft MHA2 4 September 2024
lk.4wWH6m
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$0$
$1qGDh0w1ZGyaAt34nKnm06yYJ8o=
Hex: d6a183874c35646c9a02ddf89ca9e6d3ac9827ca
MHA2 - Base algo 'sha1',
Input 'The quick brown fox jumps over the lazy dog',
Salt '', Iterations 1
MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=1$$9zbRpQFxyeyoJj0keA
dMpjXdvuK
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$1$
$B/dTrSHz+g+qLl2mgCfOrlZfxwM=
Hex: 07f753ad21f3fa0faa2e5da68027ceae565fc703
MHA2 - Base algo 'sha1',
Input 'The quick brown fox jumps over the lazy dog',
Salt '', Iterations 2
MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=2$$gGCiACHhKqZgNFztpF
zsncKMCTS
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$2$
$iIEkCEJjMsbiPH/vrH/upeMOEVU=
Hex: 88812408426332c6e23c7fefac7feea5e30e1155
MHA2 - Base algo 'sha1',
Input 'The quick brown fox jumps over the lazy dog',
Salt 'salt', Iterations 0
MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=0$a0Dqb8$EFuadpjXUzjJ
BNVfZHS.iQ/.dM2
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$0$
c2FsdA==$GHwcfrlZW/lLDPXhbJU0kS10fO4=
Hex: 187c1c7eb9595bf94b0cf5e16c9534912d747cee
MHA2 - Base algo 'sha1',
Input 'The quick brown fox jumps over the lazy dog',
Salt 'salt', Iterations 1
MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=1$a0Dqb8$fMnarhbJV/XF
qzP38t7RJEdHKJ2
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$1$
c2FsdA==$hOpctjdLX1ZHs/R5Av9TLGfJML4=
Hex: 84ea5cb6374b5f5647b3f47902ff532c67c930be
MHA2 - Base algo 'sha1',
Input 'The quick brown fox jumps over the lazy dog',
Salt 'salt', Iterations 2
MCF: $1.3.6.1.4.1.37476.3.2.1.2$a=sha1,i=2$a0Dqb8$dECLjkOyRDCv
5W9QS4Qm3ZgXRh2
HSN: 1.3.6.1.4.1.37476.3.2.1.2$1.3.6.1.4.1.37476.3.2.1.99.5$2$
c2FsdA==$fGENlmQ+TFEx7YBSU6So5biZTj4=
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Hex: 7c610d96643e4c5131ed805253a4a8e5b8994e3e
5 Reference implementation
// Implementation in PHP, with hex output define('MHA2_K', chr(0x24).chr(0x12).chr(0x19).chr(0x87)); define('MHA2_P', chr(0x12).chr(0x24).chr(0x19).chr(0x87)); define('MHA2_Q', chr(0x19).chr(0x87).chr(0x12).chr(0x24)); function mha2($message, $salt, $iterations, $base_algo) { assert($iterations>=0); $a = ''; $b = ''; $c = ''; for ($i=0; $i<=$iterations; $i++) { // run $iterations+1 times $a = hash($base_algo, MHA2_P.$a.$message.$salt.MHA2_Q, true/*binary*/); $b = hash($base_algo, MHA2_Q.$salt.$message.$b.MHA2_P, true/*binary*/); $c .= MHA2_K.$message.$salt; } $c = hash($base_algo, $c, true/*binary*/); return bin2hex($a ^ $b ^ $c); } // Framework for PHP, with MCF output and auto-generated salt: // https://github.com/danielmarschall/php_utils/blob/master/ // vts_crypt.inc.php include 'vts_crypt.inc.php'; $hash = vts_password_hash($data, PASSWORD_VTS_MHA2, ['algo'=>'sha1', 'salt_length'=>16, 'iterations'=>1987]); assert(vts_password_verify($data, $hash));6 Security Considerations
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. - The output length of MHA2(i, s, x) is equal to the output length of H(z). - MHA2(i, '', s & x) != MHA2(i, s, x) != MHA2(i, '', x & s). - It is recommended not to use i=0. - P, Q and K are chosen to arbitrary data . It can be chosen to a different value, but should not be empty. Marschall [Page 8]VTS/WF STD. 6 ViaThinkSoft MHA2 4 September 2024
- P should never be equal to Q, otherwise, A(i,s,x) could become
equal to B(i,s,x).
Possible "optimizations" (vulnerabilities) can be done if P&Q = Q&P:
a) If i = 0 and s&x = x&s:
=> A(0, s, x) = B(0, s, x)
=> MHA2(0, s, x) = H(K&x&s)
b) If s&x='' (s='' and x=''):
=> A(i, '', '') = B(i, '', '')
=> MHA2(i, '', '') = H('')
c) If z := s&x = x&s:
=> H(s&x) = H(x&s) = H(z)
=> H(s&x) = A(0,s,x) = H(z) = B(0,s,x) = H(P&x&s&Q)
= H(Q&s&x&P)
=> in A(i,s,x) and B(i,s,x),
this embedded value H(z) has to be calculated only once.
Note: s&x = x&s is true if one of the following conditions is true:
x = '' or
s = '' or
x = s
- If H(x) is compromised, MHA2 (even unsalted) would be still safe.
Examples:
i = 0, unsalted (s=''):
H(P&x&Q) = H(P&y&Q) = c
=> MHA2(0, '', x) = c xor c xor H(K&x)
= c xor c xor H(K&y)
= MHA2(0, '', y)
=> H(K&x) ?= H(K&y)
i = 1, unsalted (s=''):
H(P&x&Q) = H(P&y&Q) = c
=> MHA2(1, '', x) = H(P&c&x&Q) xor H(Q&x&c&P) xor H(K&x&K&x)
= H(P&c&y&Q) xor H(Q&y&c&P) xor H(K&y&K&y)
= MHA2(1, '', y)
=> H(P&c&x&Q) xor H(Q&x&c&P) xor H(K&x&K&x)
?= H(P&c&y&Q) xor H(Q&y&c&P) xor H(K&y&K&y)
i = 2, unsalted (s=''):
H(P&x&Q) = H(P&y&Q) = c
=> MHA2(2, '', x) = H(P&H(P&c&x&Q)&x&Q) xor
H(Q&x&H(Q&x&c&P)&P) xor H(K&x&K&x&K&x) =
H(P&H(P&c&y&Q)&y&Q) xor H(&Qx&H(&Qy&c&P)&P)
xor H(K&y&K&y&K&y) = MHA2(2, '', y)
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=> H(P&H(P&c&x&Q)&x&Q) xor H(Q&x&H(Q&x&c&P)&P)
xor H(K&x&K&x&K&x) ?= H(P&H(P&c&y&Q)&y&Q)
xor H(Q&x&H(Q&y&c&P)&P) xor H(K&y&K&y&K&y)
- If a high value for i is chosen, the hash will be slow. Therefore,
the creation of a rainbow table or brute force attacks will be slow
(see runtime section). On the other hand, a brute force attack could
result in a DoS if the CPU of the server is too weak.
- The salt should always be set. The salt should be a merge of an
individual (random unique) user-specific salt, a service-specific
salt and server-specific salt. s = userSalt & serviceSalt &
serverSalt
- For the third xor argument "xor C(i,s,x)" is not required, but does
probably strengten the algorithm in case that an attack can be found
where A(i,s,x) = B(i,s,x) can be enforced.
6.1 Runtime complexity
The following table will show the required executions of the hash function H(z) on given number of different values of i: ------------------ i H(z)-calls ------------------ 0 3 1 5 2 7 3 9 n 2n+3 ------------------ Marschall [Page 10]VTS/WF STD. 6 ViaThinkSoft MHA2 4 September 2024
7 RA Considerations
OID: 1.3.6.1.4.1.37476.3.2.1.2 WEID: weid:pen:SX0-3-2-1-2-9 ASN1: { iso(1) identified-organization(3) dod(6) internet(1) private(4) enterprise(1) 37476 specifications(3) algorithm(2) hash(1) mha2(2) } IRI: /.../Specifications/Algorithm/Hash/MHA2 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 + ... 224 + ... 256 + ... 384 + ... 512 + ... ... 224 + ... ... 256 + sha3(7), IRI SHA3 + ... 224 + ... 256 + ... 384 + ... 512 + shake(8), IRI SHAKE + ... 128 + ... 2568 References
6.1 Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, <https://www.rfc-editor.org/info/rfc2119>. Marschall [Page 11]VTS/WF STD. 6 ViaThinkSoft MHA2 4 September 2024