From Newsgroup: sci.crypt

Dear sci.math, sci.crypt, and japan.sci.math,

Please excuse the English.

The next step [1] in my Cryptohack adventure consists of using the Ton- elli-Shanks algorithm. As it happens this is not provided by Python,
nor SymPy, nor NumPy to my knowledge. It is also hard to find actual
books on this subject, written by humans, that are not copy pasta from Wikipedia. I present


https://www.betterworldbooks.com/product/detail/tonelli-shanks-algorithm-9786131148453

as a book I'm not interested in, plus it's out of stock anyway.

Now, as I'm currently trying to curb my tsundoku, I'm looking primarily
for freely available mathematical P.D.Fs., or alternatively, H.T.M.L.
articles written by humans for humans. I have deliberately /not/ read Wikipedia yet, as I have mostly found it confusing in the past.

To add insult to injury, my physical library of mathematical, and cryptographical books is not extensive enough to have this algorithm
mentioned in an index.

So, before I give up and try to read Wikipedia, or -- to my chagrin --
ask an L.L.M., is there a wizard of sci.math, sci.crypt, or japan.sci.
math who knows a human written source on this subject that is /not/ --
again -- a copy pasta of Wikipedia?


Best wishes, and happy mathematics!


[1] In the previous step, after implementing my own Jacobi Symbol, I
cheated, and used the built-in pow( a, b, p ) function for fast modular arithmetic, instead of implementing my own.
--
Johann | email: invalid -> com | http://www.myrkraverk.com/blog/
I'm not from the Internet, I just work there. | via XS News https://bsky.app/profile/myrkraverk.bsky.social | for ( ;; ) _:;

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From Newsgroup: sci.crypt

On 9/22/2026 12:03 AM, Johann 'Myrkraverk' Oskarsson wrote:

Dear sci.math, sci.crypt, and japan.sci.math,

Please excuse the English.

The next step [1] in my Cryptohack adventure consists of using the Ton- elli-Shanks algorithm.-a As it happens this is not provided by Python,
nor SymPy, nor NumPy to my knowledge.-a It is also hard to find actual
books on this subject, written by humans, that are not copy pasta from Wikipedia.-a I present

https://www.betterworldbooks.com/product/detail/tonelli-shanks- algorithm-9786131148453

as a book I'm not interested in, plus it's out of stock anyway.

Now, as I'm currently trying to curb my tsundoku, I'm looking primarily
for freely available mathematical P.D.Fs., or alternatively, H.T.M.L. articles written by humans for humans.-a I have deliberately /not/ read Wikipedia yet, as I have mostly found it confusing in the past.

To add insult to injury, my physical library of mathematical, and cryptographical books is not extensive enough to have this algorithm mentioned in an index.

So, before I give up and try to read Wikipedia, or -- to my chagrin --
ask an L.L.M., is there a wizard of sci.math, sci.crypt, or japan.sci.
math who knows a human written source on this subject that is /not/ --
again -- a copy pasta of Wikipedia?

Best wishes, and happy mathematics!

[1] In the previous step, after implementing my own Jacobi Symbol, I
cheated, and used the built-in pow( a, b, p ) function for fast modular arithmetic, instead of implementing my own.

Ok, so /after/ posting this, I came across lecture notes about a diff-
erent algorithm that does the same thing with matrices. I'll leave that
one for later. It's Perelta's Algorithm, and the lecture notes are at

https://gyarmatikati.web.elte.hu/targyak/computational/szamiteng10.pdf

which references


https://archive.org/details/HistoryOfTheTheoryOfNumbersI/page/215/mode/1up

for the original Tonelli algorithm. For the curious, Perelta's is at

https://empslocal.ex.ac.uk/people/staff/rjchapma/courses/nt13/peralta.pdf

as well.

Chances are, these are also listed as references in Wikipedia, but I
haven't bothered to try to read it yet. I have personal experience of
finding erroneous information due to over-reliance on outdated scien-
tific resources, so if any of you know better references, please share.


Best wishes, and happy Perelta's Algorithm!
--
Johann | email: invalid -> com | http://www.myrkraverk.com/blog/
I'm not from the Internet, I just work there. | via XS News https://bsky.app/profile/myrkraverk.bsky.social | for ( ;; ) _:;
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From Newsgroup: sci.crypt

Johann 'Myrkraverk' Oskarsson wrote:

Dear sci.math, sci.crypt, and japan.sci.math,

Please excuse the English.

The next step [1] in my Cryptohack adventure consists of using the Ton- elli-Shanks algorithm.-a As it happens this is not provided by Python,
nor SymPy, nor NumPy to my knowledge.-a It is also hard to find actual
books on this subject, written by humans, that are not copy pasta from Wikipedia.-a I present

https://www.betterworldbooks.com/product/detail/tonelli-shanks-algorithm-9786131148453

as a book I'm not interested in, plus it's out of stock anyway.

Now, as I'm currently trying to curb my tsundoku, I'm looking primarily

I had a tsundoku situation but then the place did a bedbug crackdown.
They swiped all my books I'd built up (it was what kept me sane during confinement), maybe $800 worth of books, and about two weeks later told
me they weren't giving them back. That's the last time I built up books
I wouldn't read. Now I'm particular about what I pick up. I was reading yarros' 4th wing & got sick of it & secretly slipped it onto the library shelves. Someone left Baldacci's The Whole Truth around and I picked it
up, got tired of it and secretly slipped it onto the library shelves.
--
Roland the Headless Thompson Gunner
Norway's Favorite Son
They can still see his headless body stalkin' through the night
And the muzzle flash of Roland's Thompson gun
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From Newsgroup: sci.crypt

On 9/22/2026 12:21 AM, Johann 'Myrkraverk' Oskarsson wrote:

On 9/22/2026 12:03 AM, Johann 'Myrkraverk' Oskarsson wrote:

Dear sci.math, sci.crypt, and japan.sci.math,

Please excuse the English.

The next step [1] in my Cryptohack adventure consists of using the Ton-
elli-Shanks algorithm.-a As it happens this is not provided by Python,
nor SymPy, nor NumPy to my knowledge.-a It is also hard to find actual
books on this subject, written by humans, that are not copy pasta from
Wikipedia.-a I present


https://www.betterworldbooks.com/product/detail/tonelli-shanks-
algorithm-9786131148453

as a book I'm not interested in, plus it's out of stock anyway.

Now, as I'm currently trying to curb my tsundoku, I'm looking primarily
for freely available mathematical P.D.Fs., or alternatively, H.T.M.L.
articles written by humans for humans.-a I have deliberately /not/ read
Wikipedia yet, as I have mostly found it confusing in the past.

To add insult to injury, my physical library of mathematical, and
cryptographical books is not extensive enough to have this algorithm
mentioned in an index.

So, before I give up and try to read Wikipedia, or -- to my chagrin --
ask an L.L.M., is there a wizard of sci.math, sci.crypt, or japan.sci.
math who knows a human written source on this subject that is /not/ --
again -- a copy pasta of Wikipedia?


Best wishes, and happy mathematics!


[1] In the previous step, after implementing my own Jacobi Symbol, I
cheated, and used the built-in pow( a, b, p ) function for fast modular
arithmetic, instead of implementing my own.

Ok, so /after/ posting this, I came across lecture notes about a diff-
erent algorithm that does the same thing with matrices.-a I'll leave that
one for later.-a It's Perelta's Algorithm, and the lecture notes are at

-a https://gyarmatikati.web.elte.hu/targyak/computational/szamiteng10.pdf

which references

https://archive.org/details/HistoryOfTheTheoryOfNumbersI/page/215/mode/1up

for the original Tonelli algorithm.-a For the curious, Perelta's is at

-a https://empslocal.ex.ac.uk/people/staff/rjchapma/courses/nt13/ peralta.pdf

as well.

Chances are, these are also listed as references in Wikipedia, but I
haven't bothered to try to read it yet.-a I have personal experience of finding erroneous information due to over-reliance on outdated scien-
tific resources, so if any of you know better references, please share.

Best wishes, and happy Perelta's Algorithm!

Well, chasing down the reference in the /History of the Theory of
Numbers/, volume I, I found

https://babel.hathitrust.org/cgi/pt?id=mdp.39015047637247&seq=354

which some of you wizards might find interesting. Aber ich spreche nur
sehr klein Deutsch.


Best wishes, and happy studies of German in sci.math!
--
Johann | email: invalid -> com | http://www.myrkraverk.com/blog/
I'm not from the Internet, I just work there. | via XS News https://bsky.app/profile/myrkraverk.bsky.social | for ( ;; ) _:;
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From Newsgroup: sci.crypt

On 9/22/2026 12:38 AM, Lane W wrote:

Johann 'Myrkraverk' Oskarsson wrote:

Dear sci.math, sci.crypt, and japan.sci.math,

Please excuse the English.

The next step [1] in my Cryptohack adventure consists of using the Ton-
elli-Shanks algorithm.-a As it happens this is not provided by Python,
nor SymPy, nor NumPy to my knowledge.-a It is also hard to find actual
books on this subject, written by humans, that are not copy pasta from
Wikipedia.-a I present


https://www.betterworldbooks.com/product/detail/tonelli-shanks-
algorithm-9786131148453

as a book I'm not interested in, plus it's out of stock anyway.

Now, as I'm currently trying to curb my tsundoku, I'm looking primarily

I had a tsundoku situation but then the place did a bedbug crackdown.
They swiped all my books I'd built up (it was what kept me sane during confinement), maybe $800 worth of books, and about two weeks later told
me they weren't giving them back. That's the last time I built up books
I wouldn't read. Now I'm particular about what I pick up. I was reading yarros' 4th wing & got sick of it & secretly slipped it onto the library shelves. Someone left Baldacci's The Whole Truth around and I picked it
up, got tired of it and secretly slipped it onto the library shelves.

Dear Lane,

I had planned to write you a lengthier letter later on, but I'll let
this suffice for the time being.

You might want to look into diatomaceous earth. I will now forthwith
put it on a higher priority list for distribution in my library. Sadly,
that is not something I can undertake immediately, so it'll will have to
be in the priority queue.

I wanted to write more about preservation of rare books, of which I have fortunately none [1], and do not have the budget to buy rare 19th cen-
tury books of mathematics, but will let this paragraph do for now.


Best wishes, and happy securing your rare books!

[1] At least, I don't think I do; maybe Organick qualifies?
--
Johann | email: invalid -> com | http://www.myrkraverk.com/blog/
I'm not from the Internet, I just work there. | via XS News https://bsky.app/profile/myrkraverk.bsky.social | for ( ;; ) _:;
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