[Cryptography] DuraShare: BIP39-native secret sharing with full manual fallback

[Renato Schiavinato Lopez]

I'm happy to share that a pre-print version of DuraShare's paper is available.

I'd love to hear your comments, review, or critique.

https://eprint.iacr.org/2026/2300

DuraShare: BIP39-native secret sharing with full manual fallback
Jeroen van de Graaf, DCC / UFMG
Renato Schiavinato Lopez, Grifortis

Abstract
BIP39 is a Bitcoin standard that turns a wallet's random seed of size
between 128 and 256 bits into a human-readable sequence of 12 to 24
words, taken from a fixed 2048-word list. Each word corresponds to an
index in that list. DuraShare allows the holder of this sequence to
split it among n Sharekeepers, each of whom receives one share. Any
subset of k Sharekeepers can combine their shares and reconstruct the
original sequence, whereas k-1 colluding Sharekeepers obtain no
(Shannon) information.

For everyday convenience we adopt a software-assisted model, while
ensuring that a full manual fallback remains feasible for recovery,
requiring nothing beyond paper, a calculator, and specific
instructions. This matters because Sharekeepers may be family members
or lawyers unfamiliar with crypto-technology, called upon only decades
later, when no specific vendor, software, or hardware can be assumed
to still exist.

DuraShare combines three existing, well-established cryptographic
techniques: (1) Shamir Secret Sharing over GF(2053), the smallest
prime larger than 2048; (2) 2D error detection, applying row and
column checksums to each share to protect the data against
transcription errors and physical damage; and (3) a simple affine
inner-product MAC over GF(2053) to authenticate each share, preventing
a Sharekeeper from tampering without being detected.

Best regards,

Renato