📅 Original date posted:2022-07-09
📝 Original message:Thanks, Zac!
I indeed did get the napkin math very wrong. I now get around 10^30 total
possible phrases, which would take an impossibly long time to brute force.
So, it is less entropy but probably still sufficient for low-stakes usage.
James
On Sat, Jul 9, 2022 at 10:31 PM Zac Greenwood <zachgrw at gmail.com> wrote:
> Sorting a seed alphabetically reduces entropy by ~29 bits.
>
> A 12-word seed has (12, 12) permutations or 479 million, which is ln(469m)
> / ln(2) ~= 29 bits of entropy. Sorting removes this entropy entirely,
> reducing the seed entropy from 128 to 99 bits.
>
> Zac
>
>
> On Fri, 8 Jul 2022 at 16:09, James MacWhyte via bitcoin-dev <
> bitcoin-dev at lists.linuxfoundation.org> wrote:
>
>>
>> What do you do if the "first" word (of 12), happens to be the last word
>>> in the list alphabetically?
>>>
>>
>> That couldn't happen. If one word is the very last from the wordlist, it
>> would end up at the end of your mnemonic once you rearrange your 12 words
>> alphabetically.
>>
>> However!
>>
>> (@vjudeu) Choosing 11 random words and then sorting them alphabetically
>> before assigning a checksum would reduce entropy considerably. If you think
>> about it, to bruteforce the entire keyspace one would only need to come up
>> with every possible combination of 11 words + 1 checksum. I'm not the best
>> at napkin math, but I think that leaves you with around 10 trillion
>> combinations, which would only take a couple months to exhaust with
>> hardware that can do 1 million guesses per second.
>>
>>
>> James
>> _______________________________________________
>> bitcoin-dev mailing list
>> bitcoin-dev at lists.linuxfoundation.org
>> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>>
>
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James MacWhyte [ARCHIVE] /
npub12t…pye9h
2023-06-07 23:11:17
in reply to nevent1q…7mup
Author Public Key
npub12tjaqer27049ejmvf0f3yd7kq6p93gg6ecavgrczge4rlzf59y5q2pye9hSeen on
wss://relay.nostr.bandPublished at
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"content": "📅 Original date posted:2022-07-09\n📝 Original message:Thanks, Zac!\n\nI indeed did get the napkin math very wrong. I now get around 10^30 total\npossible phrases, which would take an impossibly long time to brute force.\nSo, it is less entropy but probably still sufficient for low-stakes usage.\n\nJames\n\n\nOn Sat, Jul 9, 2022 at 10:31 PM Zac Greenwood \u003czachgrw at gmail.com\u003e wrote:\n\n\u003e Sorting a seed alphabetically reduces entropy by ~29 bits.\n\u003e\n\u003e A 12-word seed has (12, 12) permutations or 479 million, which is ln(469m)\n\u003e / ln(2) ~= 29 bits of entropy. Sorting removes this entropy entirely,\n\u003e reducing the seed entropy from 128 to 99 bits.\n\u003e\n\u003e Zac\n\u003e\n\u003e\n\u003e On Fri, 8 Jul 2022 at 16:09, James MacWhyte via bitcoin-dev \u003c\n\u003e bitcoin-dev at lists.linuxfoundation.org\u003e wrote:\n\u003e\n\u003e\u003e\n\u003e\u003e What do you do if the \"first\" word (of 12), happens to be the last word\n\u003e\u003e\u003e in the list alphabetically?\n\u003e\u003e\u003e\n\u003e\u003e\n\u003e\u003e That couldn't happen. If one word is the very last from the wordlist, it\n\u003e\u003e would end up at the end of your mnemonic once you rearrange your 12 words\n\u003e\u003e alphabetically.\n\u003e\u003e\n\u003e\u003e However!\n\u003e\u003e\n\u003e\u003e (@vjudeu) Choosing 11 random words and then sorting them alphabetically\n\u003e\u003e before assigning a checksum would reduce entropy considerably. If you think\n\u003e\u003e about it, to bruteforce the entire keyspace one would only need to come up\n\u003e\u003e with every possible combination of 11 words + 1 checksum. I'm not the best\n\u003e\u003e at napkin math, but I think that leaves you with around 10 trillion\n\u003e\u003e combinations, which would only take a couple months to exhaust with\n\u003e\u003e hardware that can do 1 million guesses per second.\n\u003e\u003e\n\u003e\u003e\n\u003e\u003e James\n\u003e\u003e _______________________________________________\n\u003e\u003e bitcoin-dev mailing list\n\u003e\u003e bitcoin-dev at lists.linuxfoundation.org\n\u003e\u003e https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev\n\u003e\u003e\n\u003e\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: \u003chttp://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20220710/26e276d1/attachment-0001.html\u003e",
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