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From: Steven Hatzakis <shatzakis@gmail.com>
Date: Tue, 4 Dec 2018 14:42:42 +0200
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Cc: bitcoin-dev@lists.linuxfoundation.org
Subject: Re: [bitcoin-dev] Proposal for Palindromic (Reversible) Mnemonics
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Thanks, James and Joseph, for the feedback,
It has been a fun experiment!

I just want to note that the plausible deniability was not the motive but
just an example use-case, there are perhaps other use-cases that would be
on the user to decide. I think having a mnemonic that is also reversible
could be useful for other reasons - convenience related perhaps.
*Re security:* I am still not convinced entirely that security is reduced
at all because one still has to search through all entropy in the range
of 2^128 to see whether any of those are reversible (unless there is a way
to only search the field of 2^124 that are reversible, which I don't think
is possible because the hash-derived checksum cannot be determined before
hashing, only afterward). Therefore, security should still be 2^128 for a
12-word mnemonic whether it is reversible or not (as one in every 16 people
that already have one (12-word) is reversible, they just might not realize
it, so we can't say those are less secure).

Best regards,

On Tue, Dec 4, 2018 at 2:16 PM James MacWhyte <macwhyte@gmail.com> wrote:

> I agree with Joseph. If you want plausible deniability, it would be bette=
r
> to simply hide the funds somewhere in the HD chain. Same if you want a
> second vault tied to the same phrase.
>
> You are reducing security by eliminating all entropy that doesn't fit the
> reversible criteria, although in practice it doesn't make a difference
> because the numbers are so big. However, it doesn't seem like a very usef=
ul
> feature to have.
>
> Thanks for doing all that work though, it was fun to read about your idea
> and what you found out through experimenting!
>
> James
>
>
> On Mon, Dec 3, 2018 at 1:00 PM Joseph Gleason =E2=91=88 via bitcoin-dev <
> bitcoin-dev@lists.linuxfoundation.org> wrote:
>
>> I have a suggestion.  If you are concerned about plausible deniability,
>> then it might make sense to just have the single mnemonic seed lead to a
>> single xprv key (as usual) and then do a private key derivation from tha=
t
>> based on a password string.  The password can be simple, as it is based =
on
>> the security of the seed, just as long as the user feels they need for
>> deniability.
>>
>> A simple reverse scheme like you describe would just be another thing a
>> person would know to check if given some seed so I don't see it as
>> providing much value, but I could be missing something.
>>
>> On Mon, Dec 3, 2018 at 10:45 AM Steven Hatzakis via bitcoin-dev <
>> bitcoin-dev@lists.linuxfoundation.org> wrote:
>>
>>> Hi All,
>>>
>>> I've developed a method to check if a mnemonic is also valid when the
>>> words are put into reverse order (not the entropy), where a given 12 or
>>> 24-word mnemonic could be valid both in little endian and big endian
>>> format. I've coined these "Palindromic Mnemonics", but perhaps more
>>> user-friendly is "reversible mnemonics."
>>>
>>> Purpose:
>>> A checksum-valid reversible mnemonic allows two separate vaults to be
>>> connected to the same mnemonic string of words, where all a users must =
do
>>> is enter the words in reverse order (the last word becomes first, secon=
d to
>>> last becomes second, and so on) to access the secondary (reversed words=
)
>>> vault. This utility could provide multiple use-cases, including related=
 to
>>> combinations with passphrases and plausible deniability, as well as
>>> conveniences for those wishing to use a separate vault tied to the same
>>> string of words.
>>>
>>> Security:
>>> For any randomly generated 12-word mnemonic (128-bits of security) the
>>> chances of it also being reversible are 1/16 (I believe), as a total of=
 4
>>> bit positions must be identical (4 bits from the normal mnemonic and
>>> another 4 bits from the reversed string must match). For a 24-word
>>> mnemonic, those values increase to 8 bits which need to match 8 bits fr=
om
>>> the reversed string, leading to about 1 in every 256 mnemonics also bei=
ng
>>> reversible. While the message space of valid reversible mnemonics shoul=
d be
>>> 2^124 for 12 words, that search must still be conducted over a field of
>>> 2^128, as the hash-derived checksum values otherwise prevent a way to
>>> deterministically find valid reversible mnemonics without first going
>>> through invalid reversible ones to check. I think others should chime i=
n on
>>> whether they believe there is any security loss, in terms of entropy bi=
ts
>>> (assuming the initial 128 bits were generated securely). I estimate at =
most
>>> it would be 4-bits of loss for a 12-word mnemonic, but only if an attac=
ker
>>> had a way to search only the space of valid reversible mnemonics (2**12=
4)
>>> which I don't think is feasible (could be wrong?). There could also be
>>> errors in my above assumptions, this is a work in progress and sharing =
it
>>> here to solicit initial feedback/interest.
>>>
>>> I've already written the code that can be used for testing (on GitHub
>>> user @hatgit), and when run from terminal/command prompt it is pretty f=
ast
>>> to find a valid reversible mnemonics, whereas on IDLE in Python on a 32=
-bit
>>> and 64-bit machine it could take a few seconds for 12 words and sometim=
es
>>> 10 minutes to find a valid 24-word reversible mnemonic.
>>> Example 12 words reversible (with valid checksum each way):
>>>
>>> limit exact seven clarify utility road image fresh leg cabbage hint can=
oe
>>>
>>> And Reversed:
>>>
>>> canoe hint cabbage leg fresh image road utility clarify seven exact lim=
it
>>>
>>>
>>> Example 24 reversible:
>>>
>>> favorite uncover sugar wealth army shift goose fury market toe message
>>> remain direct arrow duck afraid enroll salt knife school duck sunny gru=
nt
>>> argue
>>>
>>> And reversed:
>>>
>>> argue grunt sunny duck school knife salt enroll afraid duck arrow direc=
t
>>> remain message toe market fury goose shift army wealth sugar uncover
>>> favorite
>>>
>>>
>>> My two questions 1) are how useful could this be for
>>> you/users/devs/service providers etc.. and 2) is any security loss
>>> occurring and whether it is negligible or not?
>>>
>>> Best regards,
>>>
>>> Steven Hatzakis
>>> _______________________________________________
>>> bitcoin-dev mailing list
>>> bitcoin-dev@lists.linuxfoundation.org
>>> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>>>
>> _______________________________________________
>> bitcoin-dev mailing list
>> bitcoin-dev@lists.linuxfoundation.org
>> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>>
>

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<div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-family:arial,he=
lvetica,sans-serif">Thanks, James and Joseph, for the feedback,</div><div c=
lass=3D"gmail_default" style=3D"font-family:arial,helvetica,sans-serif">It =
has been a fun experiment!=C2=A0<br></div><div class=3D"gmail_default" styl=
e=3D"font-family:arial,helvetica,sans-serif"><br></div><div class=3D"gmail_=
default" style=3D"font-family:arial,helvetica,sans-serif">I just want to no=
te that the plausible deniability was not the motive but just an example us=
e-case, there are perhaps other use-cases that would be on the user to deci=
de. I think having a mnemonic that is also reversible could be useful for o=
ther reasons - convenience related perhaps.=C2=A0</div><div class=3D"gmail_=
default" style=3D"font-family:arial,helvetica,sans-serif"><b>Re security:</=
b> I am still not convinced entirely that security is reduced at all becaus=
e one still has to search through all entropy in the range of=C2=A02^128 to=
 see whether any of those are reversible (unless there is a way to only sea=
rch the field of 2^124 that are reversible, which I don&#39;t think is poss=
ible because the hash-derived checksum=C2=A0cannot be determined before has=
hing, only afterward). Therefore, security should still be 2^128 for a 12-w=
ord mnemonic whether it is reversible or=C2=A0not (as one in every 16 peopl=
e that already have one (12-word) is reversible, they just might not realiz=
e it, so we can&#39;t say those are less secure).=C2=A0</div><div class=3D"=
gmail_default" style=3D"font-family:arial,helvetica,sans-serif"><br></div><=
div><div dir=3D"ltr" class=3D"gmail_signature" data-smartmail=3D"gmail_sign=
ature"><div dir=3D"ltr"><div><div dir=3D"ltr"><div style=3D"font-size:12.8p=
x;font-family:arial,helvetica,sans-serif"><span>Best regards,</span></div><=
/div></div></div></div></div><br><div class=3D"gmail_quote"><div dir=3D"ltr=
">On Tue, Dec 4, 2018 at 2:16 PM James MacWhyte &lt;<a href=3D"mailto:macwh=
yte@gmail.com">macwhyte@gmail.com</a>&gt; wrote:<br></div><blockquote class=
=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd=
ing-left:1ex"><div dir=3D"ltr">I agree with Joseph. If you want plausible d=
eniability, it would be better to simply hide the funds somewhere in the HD=
 chain. Same if you want a second vault tied to the same phrase.<div><br></=
div><div>You are reducing security by eliminating all entropy that doesn&#3=
9;t fit the reversible criteria, although in practice it doesn&#39;t make a=
 difference because the numbers are so big. However, it doesn&#39;t seem li=
ke a very useful feature to have.<div><br></div><div>Thanks for doing all t=
hat work though, it was fun to read about your idea and what you found out =
through experimenting!</div><div><br clear=3D"all"><div><div dir=3D"ltr" cl=
ass=3D"m_6668330300381286486gmail_signature" data-smartmail=3D"gmail_signat=
ure"><div dir=3D"ltr"><div>James<br></div></div></div></div><br></div></div=
></div><br><div class=3D"gmail_quote"><div dir=3D"ltr">On Mon, Dec 3, 2018 =
at 1:00 PM Joseph Gleason =E2=91=88 via bitcoin-dev &lt;<a href=3D"mailto:b=
itcoin-dev@lists.linuxfoundation.org" target=3D"_blank">bitcoin-dev@lists.l=
inuxfoundation.org</a>&gt; wrote:<br></div><blockquote class=3D"gmail_quote=
" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><=
div dir=3D"ltr">I have a suggestion.=C2=A0 If you are concerned about plaus=
ible deniability, then it might make sense to just have the single mnemonic=
 seed lead to a single xprv key (as usual) and then do a private key deriva=
tion from that based on a password string.=C2=A0 The password can be simple=
, as it is based on the security of the seed, just as long as the user feel=
s they need for deniability.<div><br></div><div>A simple reverse scheme lik=
e you describe would just be another thing a person would know to check if =
given some seed so I don&#39;t see it as providing much value, but I could =
be missing something.</div></div><br><div class=3D"gmail_quote"><div dir=3D=
"ltr">On Mon, Dec 3, 2018 at 10:45 AM Steven Hatzakis via bitcoin-dev &lt;<=
a href=3D"mailto:bitcoin-dev@lists.linuxfoundation.org" target=3D"_blank">b=
itcoin-dev@lists.linuxfoundation.org</a>&gt; wrote:<br></div><blockquote cl=
ass=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;p=
adding-left:1ex"><div dir=3D"ltr"><div dir=3D"ltr"><div dir=3D"ltr"><div di=
r=3D"ltr"><div><p style=3D"font-family:-apple-system,system-ui,&quot;Segoe =
UI&quot;,Helvetica,Arial,sans-serif,&quot;Apple Color Emoji&quot;,&quot;Seg=
oe UI Emoji&quot;,&quot;Segoe UI Symbol&quot;;box-sizing:border-box;margin-=
bottom:16px;color:rgb(36,41,46);font-size:14px;margin-top:0px">Hi All,=C2=
=A0</p><p style=3D"font-family:-apple-system,system-ui,&quot;Segoe UI&quot;=
,Helvetica,Arial,sans-serif,&quot;Apple Color Emoji&quot;,&quot;Segoe UI Em=
oji&quot;,&quot;Segoe UI Symbol&quot;;box-sizing:border-box;margin-bottom:1=
6px;color:rgb(36,41,46);font-size:14px;margin-top:0px">I&#39;ve developed a=
 method to check if a mnemonic is also valid when the words are put into re=
verse order (not the entropy), where a given 12 or 24-word mnemonic could b=
e valid both in little endian and big endian format. I&#39;ve coined these =
&quot;Palindromic Mnemonics&quot;, but perhaps more user-friendly is &quot;=
reversible mnemonics.&quot;</p><p style=3D"font-family:-apple-system,system=
-ui,&quot;Segoe UI&quot;,Helvetica,Arial,sans-serif,&quot;Apple Color Emoji=
&quot;,&quot;Segoe UI Emoji&quot;,&quot;Segoe UI Symbol&quot;;box-sizing:bo=
rder-box;margin-bottom:16px;margin-top:0px;color:rgb(36,41,46);font-size:14=
px"><span style=3D"box-sizing:border-box;font-weight:600">Purpose:</span><b=
r style=3D"box-sizing:border-box">A checksum-valid reversible mnemonic allo=
ws two separate vaults to be connected to the same mnemonic string of words=
, where all a users must do is enter the words in reverse order (the last w=
ord becomes first, second to last becomes second, and so on) to access the =
secondary (reversed words) vault. This utility could provide multiple use-c=
ases, including related to combinations with passphrases and plausible deni=
ability, as well as conveniences for those wishing to use a separate vault =
tied to the same string of words.</p><p style=3D"font-family:-apple-system,=
system-ui,&quot;Segoe UI&quot;,Helvetica,Arial,sans-serif,&quot;Apple Color=
 Emoji&quot;,&quot;Segoe UI Emoji&quot;,&quot;Segoe UI Symbol&quot;;box-siz=
ing:border-box;margin-bottom:16px;margin-top:0px;color:rgb(36,41,46);font-s=
ize:14px"><span style=3D"box-sizing:border-box;font-weight:600">Security:</=
span><br style=3D"box-sizing:border-box">For any randomly generated 12-word=
 mnemonic (128-bits of security) the chances of it also being reversible ar=
e 1/16 (I believe), as a total of 4 bit positions must be identical (4 bits=
 from the normal mnemonic and another 4 bits from the reversed string must =
match). For a 24-word mnemonic,=C2=A0those values increase to 8 bits which =
need to match 8 bits from the reversed string, leading to about 1 in every =
256 mnemonics also being reversible. While the message space of valid rever=
sible mnemonics should be 2^<span style=3D"box-sizing:border-box">124 for 1=
2 words, that search must still be conducted over a field of 2</span><span =
style=3D"box-sizing:border-box;font-weight:600">^</span>128, as the hash-de=
rived checksum values otherwise prevent a way to deterministically find val=
id reversible mnemonics without first going through invalid reversible ones=
 to check. I think others should chime in on whether they believe there is =
any security loss, in terms of entropy bits (assuming the initial 128 bits =
were generated securely). I estimate at most it would be 4-bits of loss for=
 a 12-word mnemonic, but only if an attacker had a way to search only the s=
pace of valid reversible mnemonics (2**124) which I don&#39;t think is feas=
ible (could be wrong?). There could also be errors in my above assumptions,=
 this is a work in progress and sharing it here to solicit initial feedback=
/interest.</p><p style=3D"font-family:-apple-system,system-ui,&quot;Segoe U=
I&quot;,Helvetica,Arial,sans-serif,&quot;Apple Color Emoji&quot;,&quot;Sego=
e UI Emoji&quot;,&quot;Segoe UI Symbol&quot;;box-sizing:border-box;margin-b=
ottom:16px;margin-top:0px;color:rgb(36,41,46);font-size:14px">I&#39;ve alre=
ady written the code that can be used for testing (on GitHub user @hatgit),=
 and when run from terminal/command prompt it is pretty fast to find a vali=
d reversible mnemonics, whereas on IDLE in Python on a 32-bit and 64-bit ma=
chine it could take a few seconds for 12 words and sometimes 10 minutes to =
find a valid 24-word reversible mnemonic.=C2=A0</p>Example 12 words reversi=
ble (with valid checksum each way): <br><br>limit exact seven clarify utili=
ty road image fresh leg cabbage hint canoe<br><br>And Reversed:<br><br>cano=
e hint cabbage leg fresh image road utility clarify seven exact limit<br><b=
r><br>Example 24 reversible:<br><br>favorite uncover sugar wealth army shif=
t goose fury market toe message remain direct arrow duck afraid enroll salt=
 knife school duck sunny grunt argue</div><div><br>And reversed:</div><div>=
<br>argue grunt sunny duck school knife salt enroll afraid duck arrow direc=
t remain message toe market fury goose shift army wealth sugar uncover favo=
rite<p class=3D"m_6668330300381286486m_-575678971359378551m_671132201258651=
6752gmail-p1" style=3D"margin:0px;font-variant-numeric:normal;font-variant-=
east-asian:normal;font-stretch:normal;font-size:11px;line-height:normal;fon=
t-family:Menlo;color:rgb(0,0,0)"><span class=3D"m_6668330300381286486m_-575=
678971359378551m_6711322012586516752gmail-s1" style=3D"font-variant-ligatur=
es:no-common-ligatures"><br></span></p><p style=3D"box-sizing:border-box;ma=
rgin-bottom:16px;margin-top:0px"><span style=3D"color:rgb(36,41,46);font-fa=
mily:-apple-system,system-ui,&quot;Segoe UI&quot;,Helvetica,Arial,sans-seri=
f,&quot;Apple Color Emoji&quot;,&quot;Segoe UI Emoji&quot;,&quot;Segoe UI S=
ymbol&quot;;font-size:14px">My two questions 1) are how useful could this b=
e for you/users/devs/service providers etc.. and 2) is any security loss oc=
curring and whether it is negligible or not?</span><br></p><p style=3D"box-=
sizing:border-box;margin-bottom:16px;margin-top:0px"><span style=3D"font-fa=
mily:arial,helvetica,sans-serif;font-size:12.8px">Best regards,</span></p><=
/div><div><div dir=3D"ltr" class=3D"m_6668330300381286486m_-575678971359378=
551m_6711322012586516752gmail_signature"><div dir=3D"ltr"><div dir=3D"ltr">=
<div style=3D"font-size:12.8px;font-family:arial,helvetica,sans-serif"><spa=
n><br>Steven</span>=C2=A0<span>Hatzakis</span>=C2=A0</div><div style=3D"fon=
t-size:12.8px;font-family:arial,helvetica,sans-serif"><span class=3D"gmail_=
default" style=3D"font-family:arial,helvetica,sans-serif"> </span></div></d=
iv></div></div></div></div></div></div></div>
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bitcoin-dev@lists.linuxfoundation.org</a><br>
<a href=3D"https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev" =
rel=3D"noreferrer" target=3D"_blank">https://lists.linuxfoundation.org/mail=
man/listinfo/bitcoin-dev</a><br>
</blockquote></div>
_______________________________________________<br>
bitcoin-dev mailing list<br>
<a href=3D"mailto:bitcoin-dev@lists.linuxfoundation.org" target=3D"_blank">=
bitcoin-dev@lists.linuxfoundation.org</a><br>
<a href=3D"https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev" =
rel=3D"noreferrer" target=3D"_blank">https://lists.linuxfoundation.org/mail=
man/listinfo/bitcoin-dev</a><br>
</blockquote></div>
</blockquote></div></div>

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