Quote from: NotATether on October 03, 2021, 06:36:01 AM

Sure.

Load these 1000 example hex private keys (they are randomly generated which means don't waste your time trying to find money in these - I didn't load them).

https://pastebin.com/WNJLJd2r (too large to post here)

The script will analyze how frequently a 1 or 0 occurs in a certain bit position.

Then it uses the analysis results to estimate the probability of a 1 or 0 occurring in that position.

It also supports analyzing the probability of a sequence of bits occurring in multiple positions, but be warned that that increasing the number of positions to estimate together, uses a lot of memory (A LOT!).

This particular output makes the following result:

Code:

========== TOP 260 MOST LIKELY BIT CONFIGURATIONS (Highest probability first) ==========
Output format: <probability> [(<bit number between 0-255>, <0 or 1>), ...]
[(9.399999999999997, [(33, 0)]),
(8.600000000000009, [(127, 1)]),
(7.399999999999995, [(135, 0)]),
(7.199999999999996, [(153, 0)]),
(6.999999999999995, [(53, 0)]),
(6.600000000000006, [(142, 1)]),
(6.400000000000006, [(32, 1)]),
(6.400000000000006, [(88, 1)]),
(6.400000000000006, [(186, 1)]),
(6.399999999999995, [(124, 0)]),
(6.399999999999995, [(227, 0)]),
(6.2000000000000055, [(43, 0)]),
(5.800000000000005, [(0, 0)]),
(5.800000000000005, [(2, 0)]),
(5.800000000000005, [(9, 0)]),
(5.600000000000005, [(76, 0)]),
(5.600000000000005, [(94, 1)]),
(5.600000000000005, [(111, 0)]),
(5.600000000000005, [(137, 1)]),
(5.600000000000005, [(196, 1)]),
(5.600000000000005, [(208, 1)]),
(5.400000000000005, [(16, 1)]),
(5.400000000000005, [(247, 1)]),
(5.200000000000005, [(15, 1)]),
(5.200000000000005, [(89, 1)]),
(5.200000000000005, [(147, 1)]),
(5.200000000000005, [(170, 1)]),
(5.200000000000005, [(190, 0)]),
(5.200000000000005, [(212, 0)]),
(5.200000000000005, [(219, 0)]),
(5.000000000000004, [(3, 1)]),
(5.000000000000004, [(36, 1)]),
(5.000000000000004, [(41, 1)]),
(4.800000000000004, [(165, 1)]),
(4.800000000000004, [(169, 0)]),
(4.600000000000004, [(19, 1)]),
(4.600000000000004, [(31, 1)]),
(4.600000000000004, [(112, 1)]),
(4.600000000000004, [(140, 1)]),
(4.600000000000004, [(191, 0)]),
(4.400000000000004, [(22, 1)]),
(4.400000000000004, [(93, 1)]),
(4.200000000000004, [(18, 0)]),
(4.200000000000004, [(64, 1)]),
(4.200000000000004, [(68, 0)]),
(4.200000000000004, [(84, 0)]),
(4.200000000000004, [(174, 1)]),
(4.200000000000004, [(181, 0)]),
(4.0000000000000036, [(117, 0)]),
(4.0000000000000036, [(144, 0)]),
(4.0000000000000036, [(195, 0)]),
(4.0000000000000036, [(199, 0)]),
(4.0000000000000036, [(213, 0)]),
(4.0000000000000036, [(228, 1)]),
(3.8000000000000034, [(26, 0)]),
(3.8000000000000034, [(47, 1)]),
(3.8000000000000034, [(77, 0)]),
(3.8000000000000034, [(109, 1)]),
(3.8000000000000034, [(168, 0)]),
(3.8000000000000034, [(222, 0)]),
(3.600000000000003, [(35, 0)]),
(3.600000000000003, [(61, 1)]),
(3.600000000000003, [(92, 0)]),
(3.600000000000003, [(224, 0)]),
(3.600000000000003, [(225, 1)]),
(3.600000000000003, [(232, 0)]),
(3.400000000000003, [(1, 0)]),
(3.400000000000003, [(40, 0)]),
(3.400000000000003, [(102, 1)]),
(3.400000000000003, [(116, 1)]),
(3.400000000000003, [(188, 1)]),
(3.400000000000003, [(244, 1)]),
(3.200000000000003, [(103, 1)]),
(3.200000000000003, [(108, 0)]),
(3.200000000000003, [(129, 0)]),
(3.200000000000003, [(132, 0)]),
(3.200000000000003, [(139, 1)]),
(3.200000000000003, [(159, 1)]),
(3.200000000000003, [(238, 0)]),
(3.0000000000000027, [(7, 0)]),
(3.0000000000000027, [(10, 1)]),
(3.0000000000000027, [(25, 1)]),
(3.0000000000000027, [(45, 1)]),
(3.0000000000000027, [(72, 1)]),
(3.0000000000000027, [(85, 0)]),
(3.0000000000000027, [(98, 1)]),
(3.0000000000000027, [(99, 1)]),
(3.0000000000000027, [(157, 0)]),
(3.0000000000000027, [(180, 1)]),
(3.0000000000000027, [(185, 0)]),
(3.0000000000000027, [(206, 1)]),
(3.0000000000000027, [(242, 0)]),
(2.8000000000000025, [(23, 0)]),
(2.8000000000000025, [(82, 1)]),
(2.8000000000000025, [(160, 1)]),
(2.8000000000000025, [(173, 0)]),
(2.8000000000000025, [(175, 1)]),
(2.8000000000000025, [(204, 1)]),
(2.8000000000000025, [(210, 0)]),
(2.8000000000000025, [(216, 0)]),
(2.8000000000000025, [(250, 0)]),
(2.6000000000000023, [(63, 1)]),
(2.6000000000000023, [(83, 0)]),
(2.6000000000000023, [(97, 0)]),
(2.6000000000000023, [(107, 0)]),
(2.6000000000000023, [(164, 0)]),
(2.6000000000000023, [(233, 0)]),
(2.6000000000000023, [(235, 0)]),
(2.6000000000000023, [(237, 0)]),
(2.400000000000002, [(105, 1)]),
(2.400000000000002, [(128, 0)]),
(2.400000000000002, [(149, 1)]),
(2.400000000000002, [(158, 0)]),
(2.400000000000002, [(162, 1)]),
(2.400000000000002, [(177, 0)]),
(2.400000000000002, [(179, 1)]),
(2.400000000000002, [(245, 0)]),
(2.200000000000002, [(14, 1)]),
(2.200000000000002, [(27, 1)]),
(2.200000000000002, [(34, 0)]),
(2.200000000000002, [(46, 0)]),
(2.200000000000002, [(95, 1)]),
(2.200000000000002, [(115, 0)]),
(2.200000000000002, [(134, 0)]),
(2.200000000000002, [(146, 1)]),
(2.200000000000002, [(183, 0)]),
(2.200000000000002, [(189, 1)]),
(2.200000000000002, [(200, 0)]),
(2.200000000000002, [(205, 0)]),
(2.200000000000002, [(241, 1)]),
(2.200000000000002, [(243, 1)]),
(2.0000000000000018, [(54, 0)]),
(2.0000000000000018, [(58, 0)]),
(2.0000000000000018, [(113, 0)]),
(2.0000000000000018, [(119, 1)]),
(2.0000000000000018, [(133, 0)]),
(2.0000000000000018, [(155, 1)]),
(2.0000000000000018, [(194, 0)]),
(2.0000000000000018, [(240, 1)]),
(1.8000000000000016, [(42, 0)]),
(1.8000000000000016, [(62, 0)]),
(1.8000000000000016, [(65, 1)]),
(1.8000000000000016, [(67, 0)]),
(1.8000000000000016, [(104, 0)]),
(1.8000000000000016, [(131, 0)]),
(1.8000000000000016, [(152, 1)]),
(1.8000000000000016, [(176, 0)]),
(1.8000000000000016, [(217, 0)]),
(1.8000000000000016, [(226, 1)]),
(1.6000000000000014, [(39, 0)]),
(1.6000000000000014, [(57, 0)]),
(1.6000000000000014, [(74, 1)]),
(1.6000000000000014, [(80, 1)]),
(1.6000000000000014, [(121, 1)]),
(1.6000000000000014, [(182, 0)]),
(1.6000000000000014, [(215, 1)]),
(1.4000000000000012, [(6, 1)]),
(1.4000000000000012, [(52, 0)]),
(1.4000000000000012, [(75, 1)]),
(1.4000000000000012, [(81, 1)]),
(1.4000000000000012, [(87, 1)]),
(1.4000000000000012, [(101, 1)]),
(1.4000000000000012, [(123, 1)]),
(1.4000000000000012, [(198, 1)]),
(1.4000000000000012, [(214, 0)]),
(1.4000000000000012, [(236, 1)]),
(1.4000000000000012, [(249, 1)]),
(1.4000000000000012, [(253, 0)]),
(1.4000000000000012, [(255, 0)]),
(1.200000000000001, [(66, 1)]),
(1.200000000000001, [(78, 1)]),
(1.200000000000001, [(86, 1)]),
(1.200000000000001, [(118, 1)]),
(1.200000000000001, [(120, 1)]),
(1.200000000000001, [(130, 0)]),
(1.200000000000001, [(136, 1)]),
(1.200000000000001, [(143, 0)]),
(1.200000000000001, [(145, 0)]),
(1.200000000000001, [(148, 0)]),
(1.200000000000001, [(156, 0)]),
(1.200000000000001, [(218, 1)]),
(1.200000000000001, [(220, 1)]),
(1.0000000000000009, [(4, 1)]),
(1.0000000000000009, [(12, 1)]),
(1.0000000000000009, [(37, 0)]),
(1.0000000000000009, [(71, 0)]),
(1.0000000000000009, [(79, 0)]),
(1.0000000000000009, [(96, 0)]),
(1.0000000000000009, [(141, 1)]),
(1.0000000000000009, [(172, 0)]),
(1.0000000000000009, [(192, 0)]),
(1.0000000000000009, [(202, 0)]),
(1.0000000000000009, [(209, 1)]),
(1.0000000000000009, [(211, 0)]),
(1.0000000000000009, [(254, 1)]),
(0.8084000000000005, [(33, 0), (127, 1)]),
(0.8000000000000007, [(8, 1)]),
(0.8000000000000007, [(21, 1)]),
(0.8000000000000007, [(56, 0)]),
(0.8000000000000007, [(69, 1)]),
(0.8000000000000007, [(106, 1)]),
(0.8000000000000007, [(122, 0)]),
(0.8000000000000007, [(150, 0)]),
(0.8000000000000007, [(163, 1)]),
(0.8000000000000007, [(167, 0)]),
(0.8000000000000007, [(193, 1)]),
(0.8000000000000007, [(203, 1)]),
(0.8000000000000007, [(207, 0)]),
(0.8000000000000007, [(229, 1)]),
(0.8000000000000007, [(230, 0)]),
(0.8000000000000007, [(248, 0)]),
(0.8000000000000007, [(252, 0)]),
(0.6955999999999993, [(33, 0), (135, 0)]),
(0.6767999999999994, [(33, 0), (153, 0)]),
(0.6579999999999994, [(33, 0), (53, 0)]),
(0.6364000000000002, [(127, 1), (135, 0)]),
(0.6204000000000004, [(33, 0), (142, 1)]),
(0.6192000000000001, [(127, 1), (153, 0)]),
(0.6020000000000001, [(127, 1), (53, 0)]),
(0.6016000000000004, [(33, 0), (32, 1)]),
(0.6016000000000004, [(33, 0), (88, 1)]),
(0.6016000000000004, [(33, 0), (186, 1)]),
(0.6015999999999994, [(33, 0), (124, 0)]),
(0.6015999999999994, [(33, 0), (227, 0)]),
(0.6000000000000005, [(20, 0)]),
(0.6000000000000005, [(29, 0)]),
(0.6000000000000005, [(48, 1)]),
(0.6000000000000005, [(49, 0)]),
(0.6000000000000005, [(50, 1)]),
(0.6000000000000005, [(90, 1)]),
(0.6000000000000005, [(114, 0)]),
(0.6000000000000005, [(151, 1)]),
(0.6000000000000005, [(166, 1)]),
(0.6000000000000005, [(171, 0)]),
(0.6000000000000005, [(197, 0)]),
(0.6000000000000005, [(221, 1)]),
(0.6000000000000005, [(234, 1)]),
(0.5828000000000003, [(33, 0), (43, 0)]),
(0.567600000000001, [(127, 1), (142, 1)]),
(0.550400000000001, [(127, 1), (32, 1)]),
(0.550400000000001, [(127, 1), (88, 1)]),
(0.550400000000001, [(127, 1), (186, 1)]),
(0.5504, [(127, 1), (124, 0)]),
(0.5504, [(127, 1), (227, 0)]),
(0.5452000000000002, [(33, 0), (0, 0)]),
(0.5452000000000002, [(33, 0), (2, 0)]),
(0.5452000000000002, [(33, 0), (9, 0)]),
(0.5332000000000009, [(127, 1), (43, 0)]),
(0.5327999999999994, [(135, 0), (153, 0)]),
(0.5264000000000003, [(33, 0), (76, 0)]),
(0.5264000000000003, [(33, 0), (94, 1)]),
(0.5264000000000003, [(33, 0), (111, 0)]),
(0.5264000000000003, [(33, 0), (137, 1)]),
(0.5264000000000003, [(33, 0), (196, 1)]),
(0.5264000000000003, [(33, 0), (208, 1)]),
(0.5179999999999993, [(135, 0), (53, 0)]),
(0.5076000000000003, [(33, 0), (16, 1)]),
(0.5076000000000003, [(33, 0), (247, 1)]),
(0.5039999999999993, [(153, 0), (53, 0)]),
(0.4988000000000009, [(127, 1), (0, 0)])]

The values on the left, are probabilities of the bit positions on the left (beginning with 0 and ending at 255) being a 1 or 0 respectively (the second number in the tuple).

Normally when e.g. 40% of bits are 1, that means 60% of them are 0 (another version of this script using this algo can be found here https://gist.github.com/ZenulAbidin/63d13b05f5adda18f03ef2cab577fca3)

But I am calculating the probabilities above, a little differently here.

say 400 out of 1000 of keys have a specific bit at 1 like the example above, that would mean coefficient of 0.4 (where valid values are from 0 to 1 - likeliness of a bit being 1). 0.5 means that the bits are perfectly distributed evenly.

So I take this coefficient and subtract it by 0.5 - which gives a metric of how "chaotic" this bit is [n.b. this has nothing to do with quantum computers and all that].

Negative values here means the bit is more likely to be zero, Positive means more likely to be one. But the larger the absolute value of this result, the less "chaotic" (less likely to vary among larger sample size) this bit is.

This script multiplies these values by 2 to get a result between -1 and 1 (as opposed to -0.5 and 0.5), to allow interpretation as a percentage.

So 0% would be absolute chaos (equivalent to 50/50 probability of 0 or 1 for a given position). 100% would be no chaos at all (since the bit stays the same) and this is what the script is measuring.

<so this script in the form I showed you does not help you guess private key bits, it's just a scientific study of random numbers.>

The other script I linked in this post is using regular probabilities, not chaos percentages by the way.

Bro, Hello.

How to check only 1,2,3 pubkeys with this scrypt ? Without random ganeration, and without many publick keys ?

Thx