Rev 2303-1: Module 1 Share Booklet row data misaligned after R

[stutxo]

Rev 2303-1: Module 1 Share Booklet row data misaligned after R

Hello Bitcoin Wizards,

The Module 1 Share Booklet in the printed book, revision 2303-1-8822ef51 (2023-03-07--color.pdf / --bw.pdf on secretcodex32.com), has its row data shifted by one starting at row T.

Column C is the identity column, so it should always return the row's own C-share character. On every booklet page:

row label	column C shows	should show
R	R ✓	R
T	S ✗	T
U	T ✗	U
V	U ✗	V

The row labels correctly skip S because S is the secret index, but the row-data lookup still includes the S entry. As a result, every row after R uses the previous entry's data, and the final row's data is dropped.

Cause

The public branches don't seem to have this bug (they use a different, older booklet generator), so I'm not sure where the 2303-1 source on the site came from, but the fix for it would be the following:

showShareTable draws row labels from permNoS (31 values, excluding S) but computes the row data from perm (32 values, including S) at line 2748:

-      page exch perm 3 index get exch makeShare code exch get glyphshow
+      page exch permNoS 3 index get exch makeShare code exch get glyphshow

Rendering the patched source with Ghostscript produces a correct booklet: the identity-column invariant holds for every row, and Page A matches an independent BIP 93 Lagrange computation for all 31 rows.

Reproduce

Using the BIP 93 NAME, k=2 test vectors:

• Share A: MS12NAMEA320ZYXWVUTSRQPNMLKJHGFEDCAXRPP870HKKQRM
• Share C: MS12NAMECACDEFGHJKLMNPQRSTUVWXYZ023FTR2GDZMPY6PN
• True share D: MS12NAMEDLL4F8JLH4E5VDVULDLFXU2JHDNLSM97XVENRXEG

Deriving share D with the printed booklet instead yields:

6NAMEDLL4F8JLH4E?VDVU?X6XU0S45ACLMM47XTENEJEG

That gives 16 incorrect data characters out of 26, with another 2 positions that cannot be looked up.

Thanks!