09-20-2022, 10:13 AM
How unlikely it is to guess a Seed Phrase (12 vs 24 words)
<table> <tr><td> <a href="https://www.reddit.com/r/CryptoCurrency/comments/xipvqu/how_unlikely_it_is_to_guess_a_seed_phrase_12_vs/"> <img src="https://external-preview.redd.it/Q7ufJEw1V6klm1rsbP-zqdXu37Kd735DoVuBJElJKn4.jpg?width=640&crop=smart&auto=webp&s=a6b0e72a500821894f29b88625d6bd5b51442f0e" alt="How unlikely it is to guess a Seed Phrase (12 vs 24 words)" title="How unlikely it is to guess a Seed Phrase (12 vs 24 words)" /> </a> </td><td> <!-- SC_OFF --><div class="md"><p>Warning, contains math!</p> <h1>Repetition</h1> <p>What's the probability of NOT throwing a 6 with a die?</p> <p><a href="https://preview.redd.it/ufl8x21vuvo91.png?width=368&format=png&auto=webp&s=2c6f7e6e20c0a3190762bd389708786e9519b07b">https://preview.redd.it/ufl8x21vuvo91.png?width=368&format=png&auto=webp&s=2c6f7e6e20c0a3190762bd389708786e9519b07b</a></p> <p>What's the probabiltiy NOT throwing a 6 with a die 10 times in a row?</p> <p><a href="https://preview.redd.it/0dtjdl8guvo91.png?width=568&format=png&auto=webp&s=3e76b49752a3f4c309488dfe5ce575cf139ac016">https://preview.redd.it/0dtjdl8guvo91.png?width=568&format=png&auto=webp&s=3e76b49752a3f4c309488dfe5ce575cf139ac016</a></p> <h1>Seed with 12 words</h1> <p>We get 12 words out of a list of 2048. This gives us 2048^12 different theoretically possible seed phrases.</p> <p>The probability of failing to guess the correct seed phrase is:</p> <p><a href="https://preview.redd.it/yio6zry0uvo91.png?width=87&format=png&auto=webp&s=3f3c1a28651683223ce44c7c90521164c56a34e6">https://preview.redd.it/yio6zry0uvo91.png?width=87&format=png&auto=webp&s=3f3c1a28651683223ce44c7c90521164c56a34e6</a></p> <p>There's only 1 correct seed phrase, so we get (2048^12)-1 possibilities to not guess it. This is the result:</p> <p>The chance of not guessing the right seed is 99.99999999999999999999999999999999999998 % (that's 37 nines after the point)</p> <p>Pretty much elusive.</p> <h1>Let's use a CPU for a year (hypothetically)</h1> <p>My CPU has 16 cores that can run 32 parallel threads to guess seeds. Using private keys I got 350,000 keys per second when trying to guess 152,000 random addresses from a list (Python project). This is the math for guessing seeds using my CPU 24/7 for a whole year:</p> <p><a href="https://preview.redd.it/3cpl342swvo91.png?width=243&format=png&auto=webp&s=b5e659334aa671e3322568ca200187c3949392c8">https://preview.redd.it/3cpl342swvo91.png?width=243&format=png&auto=webp&s=b5e659334aa671e3322568ca200187c3949392c8</a></p> <p>Just like we rolled the dice 10 times we now do this 350k*150k*.... times. 60 seconds, 60 minutes, 24 hours, 365 days. This is the result:</p> <p>The chance of not guessing the right seed is 99.99999999999999999997 % (still 19 nines after the point!)</p> <h1>Okay, 1,000,000 years then</h1> <p>Not surprisingly the number of nines was reduced by 6: 99.99999999999997%</p> <p>Still absurdly unlikely and not worth the energy. Also I would be dead after 0.004% of that time span.</p> <h1>1 year of crunching against 24-word Seed</h1> <p>99.999999999999999999999999999999999999999999999999999999999994 %</p> <p>57 numbers after the point! This corresponds to roughly the same probability as guessing a private key with 256 Bit!</p> <p>/edit: Math was done with <a href="https://wolframalpha.com">wolframalpha.com</a> because crypto is too strong even for a scientific calculator</p> </div><!-- SC_ON --> submitted by <a href="https://www.reddit.com/user/ismirschlecht"> /u/ismirschlecht </a> <br/> <span><a href="https://www.reddit.com/r/CryptoCurrency/comments/xipvqu/how_unlikely_it_is_to_guess_a_seed_phrase_12_vs/">[link]</a></span> <span><a href="https://www.reddit.com/r/CryptoCurrency/comments/xipvqu/how_unlikely_it_is_to_guess_a_seed_phrase_12_vs/">[comments]</a></span> </td></tr></table>
<table> <tr><td> <a href="https://www.reddit.com/r/CryptoCurrency/comments/xipvqu/how_unlikely_it_is_to_guess_a_seed_phrase_12_vs/"> <img src="https://external-preview.redd.it/Q7ufJEw1V6klm1rsbP-zqdXu37Kd735DoVuBJElJKn4.jpg?width=640&crop=smart&auto=webp&s=a6b0e72a500821894f29b88625d6bd5b51442f0e" alt="How unlikely it is to guess a Seed Phrase (12 vs 24 words)" title="How unlikely it is to guess a Seed Phrase (12 vs 24 words)" /> </a> </td><td> <!-- SC_OFF --><div class="md"><p>Warning, contains math!</p> <h1>Repetition</h1> <p>What's the probability of NOT throwing a 6 with a die?</p> <p><a href="https://preview.redd.it/ufl8x21vuvo91.png?width=368&format=png&auto=webp&s=2c6f7e6e20c0a3190762bd389708786e9519b07b">https://preview.redd.it/ufl8x21vuvo91.png?width=368&format=png&auto=webp&s=2c6f7e6e20c0a3190762bd389708786e9519b07b</a></p> <p>What's the probabiltiy NOT throwing a 6 with a die 10 times in a row?</p> <p><a href="https://preview.redd.it/0dtjdl8guvo91.png?width=568&format=png&auto=webp&s=3e76b49752a3f4c309488dfe5ce575cf139ac016">https://preview.redd.it/0dtjdl8guvo91.png?width=568&format=png&auto=webp&s=3e76b49752a3f4c309488dfe5ce575cf139ac016</a></p> <h1>Seed with 12 words</h1> <p>We get 12 words out of a list of 2048. This gives us 2048^12 different theoretically possible seed phrases.</p> <p>The probability of failing to guess the correct seed phrase is:</p> <p><a href="https://preview.redd.it/yio6zry0uvo91.png?width=87&format=png&auto=webp&s=3f3c1a28651683223ce44c7c90521164c56a34e6">https://preview.redd.it/yio6zry0uvo91.png?width=87&format=png&auto=webp&s=3f3c1a28651683223ce44c7c90521164c56a34e6</a></p> <p>There's only 1 correct seed phrase, so we get (2048^12)-1 possibilities to not guess it. This is the result:</p> <p>The chance of not guessing the right seed is 99.99999999999999999999999999999999999998 % (that's 37 nines after the point)</p> <p>Pretty much elusive.</p> <h1>Let's use a CPU for a year (hypothetically)</h1> <p>My CPU has 16 cores that can run 32 parallel threads to guess seeds. Using private keys I got 350,000 keys per second when trying to guess 152,000 random addresses from a list (Python project). This is the math for guessing seeds using my CPU 24/7 for a whole year:</p> <p><a href="https://preview.redd.it/3cpl342swvo91.png?width=243&format=png&auto=webp&s=b5e659334aa671e3322568ca200187c3949392c8">https://preview.redd.it/3cpl342swvo91.png?width=243&format=png&auto=webp&s=b5e659334aa671e3322568ca200187c3949392c8</a></p> <p>Just like we rolled the dice 10 times we now do this 350k*150k*.... times. 60 seconds, 60 minutes, 24 hours, 365 days. This is the result:</p> <p>The chance of not guessing the right seed is 99.99999999999999999997 % (still 19 nines after the point!)</p> <h1>Okay, 1,000,000 years then</h1> <p>Not surprisingly the number of nines was reduced by 6: 99.99999999999997%</p> <p>Still absurdly unlikely and not worth the energy. Also I would be dead after 0.004% of that time span.</p> <h1>1 year of crunching against 24-word Seed</h1> <p>99.999999999999999999999999999999999999999999999999999999999994 %</p> <p>57 numbers after the point! This corresponds to roughly the same probability as guessing a private key with 256 Bit!</p> <p>/edit: Math was done with <a href="https://wolframalpha.com">wolframalpha.com</a> because crypto is too strong even for a scientific calculator</p> </div><!-- SC_ON --> submitted by <a href="https://www.reddit.com/user/ismirschlecht"> /u/ismirschlecht </a> <br/> <span><a href="https://www.reddit.com/r/CryptoCurrency/comments/xipvqu/how_unlikely_it_is_to_guess_a_seed_phrase_12_vs/">[link]</a></span> <span><a href="https://www.reddit.com/r/CryptoCurrency/comments/xipvqu/how_unlikely_it_is_to_guess_a_seed_phrase_12_vs/">[comments]</a></span> </td></tr></table>