first thoughts

2021-04-23 17:29:20 -04:00 · 2021-04-23 17:29:20 -04:00 · 09ae794176
commit 09ae794176
parent a1bb801bd3
5 changed files with 276 additions and 245 deletions
--- a/example.md
+++ b/example.md
--- a/html-worksheet.py
+++ b/html-worksheet.py
@ -0,0 +1,57 @@
+# Failed attempt at using HTML to show a table.
+#
+# - do not use
+# - particularly bad because ultimately we need this printed on paper
+# - don't be distracted by how close I got
+#
+
+def worksheet(count=5):
+    with open('worksheet.html', 'wt') as fd:
+        P = lambda *a: print(*a, file=fd)
+
+        P('''
+<html><head>
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="stylesheet" href="https://unpkg.com/purecss@2.0.5/build/pure-min.css">
+<style>
+td { text-align: center; }
+td.R { text-align: right; }
+td.L { text-align: left; }
+#bb {
+    transform: rotate(90deg) translate(33%, 0%);
+}
+</style>
+<body>
+<div id="bb" class="pure-g">
+<div class="pure-u-1">
+''')
+
+
+        P('<h2>XOR Seed Worksheet</h2>\n')
+        
+        P('<table class="pure-table pure-table-bordered"><tbody>')
+        for c in range(count):
+            dig = chr(65+c)
+            P(f'<tr class="pure-table-odd"><td rowspan=3>{dig}<td class=R>Word #' + ''.join(f'<td colspan=3>{n+1}' for n in range(24)))
+            P('<tr><td class=R>Word' + ''.join(f'<td colspan=3>' for n in range(24)))
+            P('<tr><td class=R>Hex&nbsp;Digit' + ''.join(f'<td> ' for n in range(24*3)))
+            if c:
+                if c == 1:
+                    here = 'A'
+                elif c > 2:
+                    here = '...'
+                else:
+                    here = '(' + '&oplus;'.join('%X' % (z+10-1) for z in range(1, c+1)) + ')'
+                P(f'<tr><td colspan=2 class=R>{here}&oplus;{dig}' 
+                        + ''.join(f'<td> ' for n in range((24*3)-2)) + '<td>X<td>X')
+            if c in {2, 5}:
+                if c == 2:
+                    m = 'sane people stop here'
+                else:
+                    m = 'please stop, this hurts'
+                P(f'<tr class="pure-table-odd"><td colspan=2><td colspan=99 class=L><em>{m}</em>')
+
+        P('</table>')
+
+worksheet()
+
--- a/output.pdf
+++ b/output.pdf
--- a/worksheet.html
+++ b/worksheet.html
@ -0,0 +1,40 @@
+
+<html><head>
+<meta name="viewport" content="width=device-width, initial-scale=1">
+<link rel="stylesheet" href="https://unpkg.com/purecss@2.0.5/build/pure-min.css">
+<style>
+td { text-align: center; }
+td.R { text-align: right; }
+td.L { text-align: left; }
+#bb {
+    transform: rotate(90deg) translate(33%, 0%);
+}
+</style>
+<body>
+<div id="bb" class="pure-g">
+<div class="pure-u-1">
+
+<h2>XOR Seed Worksheet</h2>
+
+<table class="pure-table pure-table-bordered"><tbody>
+<tr class="pure-table-odd"><td rowspan=3>A<td class=R>Word #<td colspan=3>1<td colspan=3>2<td colspan=3>3<td colspan=3>4<td colspan=3>5<td colspan=3>6<td colspan=3>7<td colspan=3>8<td colspan=3>9<td colspan=3>10<td colspan=3>11<td colspan=3>12<td colspan=3>13<td colspan=3>14<td colspan=3>15<td colspan=3>16<td colspan=3>17<td colspan=3>18<td colspan=3>19<td colspan=3>20<td colspan=3>21<td colspan=3>22<td colspan=3>23<td colspan=3>24
+<tr><td class=R>Word<td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3>
+<tr><td class=R>Hex&nbsp;Digit<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> 
+<tr class="pure-table-odd"><td rowspan=3>B<td class=R>Word #<td colspan=3>1<td colspan=3>2<td colspan=3>3<td colspan=3>4<td colspan=3>5<td colspan=3>6<td colspan=3>7<td colspan=3>8<td colspan=3>9<td colspan=3>10<td colspan=3>11<td colspan=3>12<td colspan=3>13<td colspan=3>14<td colspan=3>15<td colspan=3>16<td colspan=3>17<td colspan=3>18<td colspan=3>19<td colspan=3>20<td colspan=3>21<td colspan=3>22<td colspan=3>23<td colspan=3>24
+<tr><td class=R>Word<td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3>
+<tr><td class=R>Hex&nbsp;Digit<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> 
+<tr><td colspan=2 class=R>A&oplus;B<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td>X<td>X
+<tr class="pure-table-odd"><td rowspan=3>C<td class=R>Word #<td colspan=3>1<td colspan=3>2<td colspan=3>3<td colspan=3>4<td colspan=3>5<td colspan=3>6<td colspan=3>7<td colspan=3>8<td colspan=3>9<td colspan=3>10<td colspan=3>11<td colspan=3>12<td colspan=3>13<td colspan=3>14<td colspan=3>15<td colspan=3>16<td colspan=3>17<td colspan=3>18<td colspan=3>19<td colspan=3>20<td colspan=3>21<td colspan=3>22<td colspan=3>23<td colspan=3>24
+<tr><td class=R>Word<td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3>
+<tr><td class=R>Hex&nbsp;Digit<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> 
+<tr><td colspan=2 class=R>(A&oplus;B)&oplus;C<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td>X<td>X
+<tr class="pure-table-odd"><td colspan=2><td colspan=99 class=L><em>sane people stop here</em>
+<tr class="pure-table-odd"><td rowspan=3>D<td class=R>Word #<td colspan=3>1<td colspan=3>2<td colspan=3>3<td colspan=3>4<td colspan=3>5<td colspan=3>6<td colspan=3>7<td colspan=3>8<td colspan=3>9<td colspan=3>10<td colspan=3>11<td colspan=3>12<td colspan=3>13<td colspan=3>14<td colspan=3>15<td colspan=3>16<td colspan=3>17<td colspan=3>18<td colspan=3>19<td colspan=3>20<td colspan=3>21<td colspan=3>22<td colspan=3>23<td colspan=3>24
+<tr><td class=R>Word<td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3>
+<tr><td class=R>Hex&nbsp;Digit<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> 
+<tr><td colspan=2 class=R>...&oplus;D<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td>X<td>X
+<tr class="pure-table-odd"><td rowspan=3>E<td class=R>Word #<td colspan=3>1<td colspan=3>2<td colspan=3>3<td colspan=3>4<td colspan=3>5<td colspan=3>6<td colspan=3>7<td colspan=3>8<td colspan=3>9<td colspan=3>10<td colspan=3>11<td colspan=3>12<td colspan=3>13<td colspan=3>14<td colspan=3>15<td colspan=3>16<td colspan=3>17<td colspan=3>18<td colspan=3>19<td colspan=3>20<td colspan=3>21<td colspan=3>22<td colspan=3>23<td colspan=3>24
+<tr><td class=R>Word<td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3><td colspan=3>
+<tr><td class=R>Hex&nbsp;Digit<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> 
+<tr><td colspan=2 class=R>...&oplus;E<td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td> <td>X<td>X
+</table>
--- a/xor.py
+++ b/xor.py
@ -0,0 +1,163 @@
+# print some charts
+from hashlib import sha256
+from mnemonic import Mnemonic
+from random import Random
+from textwrap import TextWrapper
+
+wordlist = Mnemonic('english').wordlist
+
+WIDTH = 110
+
+def xor_table(indent=' '*8):
+    print(indent + '| XOR |' + '|'.join(' %X ' % x for x in range(16)))
+    print(indent + '|----:' + '|---'*16)
+
+    for y in range(16):
+        print(indent + '|**%X**|' % y, end='')
+        print('|'.join(' %X ' % (x^y) for x in range(16)))
+
+    print('''\
+
+
+- XOR = EOR = &oplus; = Exclusive OR [Wikipedia](https://en.wikipedia.org/wiki/Exclusive_or)
+- values in table are: x &oplus; y in hex
+- go sideways for first digit, then look down for second digit
+- in fact, doesn't matter if you do row or column first
+- example: 2 XOR 6 => 4  same as   6 XOR 2 => 4
+- any values XOR itself is zero (diagonal on this table)
+- alternative view: (x) XOR (y) = flip bits of (x) that are set in (y)
+    - XOR with zero does nothing (flips no bits)
+    - XOR with 0xF flips all four bits
+    - XOR with self flips all set bits, so gives zero
+- to XOR three values together, do (a&oplus;b)=X then (X&oplus;c)=answer
+    - right to A, down to B ... take that number, and go to that column
+    - down to C, that is answer: a &oplus; b &oplus; c
+''')
+
+def get_words(h):
+    # Apply BIP39 to convert into seed words
+    v = int.from_bytes(h, 'big') << 8
+    w = []
+    for i in range(24):
+        v, m = divmod(v, 2048)
+        w.insert(0, m)
+    assert not v
+
+    # final 8 bits are a checksum
+    w[-1] |= sha256(h).digest()[0]
+
+    return w
+
+def calc_check(words):
+    assert len(words) == 24
+    x = 0
+    for i in range(24):
+        x <<= 11
+        x |= words[i]
+    x >>= 8
+    raw = x.to_bytes(32, 'big')
+
+    cb = sha256(raw).digest()[0]
+
+    x <<= 8
+    x |= cb
+
+    return raw, (x % 0x800)
+
+def print_phrase(raw, indent=' '*4):
+
+    tw = TextWrapper(width=WIDTH, initial_indent=indent, subsequent_indent=indent)
+
+    if len(raw) == 32:
+        words = get_words(raw)
+        assert len(words) == 24
+    else:
+        words = list(raw)
+        assert len(words) in {23, 24}
+
+    x = ['%d=%s_[%03X]'%(n+1, wordlist[i],i) for n,i in enumerate(words)]
+    msg = ', '.join(x)
+    eng = [ln.replace('_', ' ') for ln in tw.wrap(msg)]
+
+    hx = ' '.join('%03X'%i for i in words)
+    
+    return eng, hx, words
+
+def worked_example(count=3):
+
+    rng = Random(123 * count)
+
+    print(f'# XOR Seed Example Using {count} Parts\n')
+
+    indent = ' '*6
+    digits = []
+    for n in range(count):
+        raw = bytearray(rng.randint(0, 255) for i in range(32))
+
+        eng, hx, words = print_phrase(raw, indent)
+
+        print(f'## Seed {n+10:X}  ({n+1} of {count})\n')
+        print('\n'.join(eng))
+        print(f'\n{indent}{n+10:X} = {hx}\n\n')
+
+        digits.append(hx)
+
+    print('## Calculation (XOR each hex digit)\n')
+    for n in range(count):
+        print(f'{indent}{n+10:X} = {digits[n]}')
+
+    xor = ''
+    for pos in range(len(digits[0]) - 2):
+        if digits[0][pos] == ' ':
+            xor += ' '
+            continue
+
+        here = 0
+        for n in range(count):
+            here ^= int(digits[n][pos], 16)
+        assert 0 <= here < 16, here
+        xor += '%X' % here
+
+    xor += 'xx'
+
+    lst = list(range(0, 100, 16)) + [23*4]
+    align = ''.join(('|' if n in lst else ' ') for n in range(len(xor)))
+    print(f'{indent}    {align}')
+
+    print(f'{indent[2:]}XOR = {xor}')
+
+
+    print('\n\n## Resulting Seed Phrase\n')
+    rw = [int(i, 16) for i in xor.split(' ')[:-1]]
+
+    eng, hx, _ = print_phrase(rw, indent)
+    print('\n'.join(eng))
+    chk = int(xor.split(' ')[-1][0], 16) * 0x100
+    print(f'\n{indent}final word between: %s [%03X] - %s [%03X]' % (
+            wordlist[chk], chk, wordlist[chk+0xff], chk+0xff))
+
+    secret, final = calc_check(rw + [chk])
+    print(f'{indent}correct final word: %s [%03X]' % (wordlist[final], final))
+
+    # check our checksum math
+    _, chk_hx, _ = print_phrase(secret, indent)
+    assert chk_hx.split(' ')[-1] == '%03X'%final 
+
+    print('''\
+- It's not possible to calculate the checksum of the final seed phrase on paper (needs SHA256).
+- But it must start with the indicated digit, and there will be only one
+  suitable choice offered by the Coldcard in that range (x00 to xFF),
+  once you have entered the other 23 words.
+- The checksum of each of the XOR-parts protects the final result, assuming your XOR
+  math is correct.
+''')
+
+
+if 1:
+    worked_example()
+
+if 1:
+    print('\n---\n\n')
+    print('## XOR Lookup Table\n\n')
+    xor_table('')
+