![](bg6.png)
et al., 2012, Figure 5) to verify that both outputs
from garbled circuit are the same. All benchmarks
without downloading boolean circuits were ran in a
single-threaded on an Intel i5 CPU 2.3GHz and 16GB
2133MHz LPDDR3 of RAM in the 13-inch (2018)
macbook pro.
Table 1: Basic information of circuits: f
mkg
, f
aux
, and f
ckd
.
f
mkg
f
aux
f
ckd
Total number of gates 847,420 796,827 507,581
Total number of wires 850,558 799,676 510,463
Table 2: Time consuming for running 20 samples.
2P-MKG 2P-CKD
Fast time 7.181s 2.688s
Slow time 7.748s 2.839s
Avg time 7.374s ± 0.14s 2.739s ± 0.04s
The bit-length of seed = 512, n = 33, and Paillier public key = 2048;
The number of base OT = 128; The half-gates scheme uses the
Hash function
[
MMO
E
(ref. (Guo et al., 2020, Section 7.3))
with the ideal cipher AES-128.
5 CONCLUSION AND
DISCUSSION
The proposed protocols comply with all BIP32 regu-
lations. We also provided a security proof in the hy-
brid model using simulation-based methods and ex-
perimental data. Theoretically, there will be risk in
leaking bits while using DualEx protocol since we
considered the worst scenario without any restric-
tions on g in the security proof. The leaking risk
can be potentially overcame by utilizing garbled cir-
cuit schemes against malicious adversaries such as
authenticated Garbling method.
REFERENCES
Bellare, M., Hoang, T., and Rogaway, P. (2012). Founda-
tions of garbled circuits. In Proceedings of the 2012
ACM Conference on Computer and Communications
Security, CCS ’12, pages 784–796. Association for
Computing Machinery.
Breitner, J. and Heninger, N. (2019). Biased Nonce Sense:
Lattice Attacks Against Weak ECDSA Signatures in
Cryptocurrencies, pages 3–20. Springer-Verlag.
Canetti, R., Gennaro, R., Goldfeder, S., Makriyannis, N.,
and Peled, U. (2020a). Uc non-interactive, proactive,
threshold ecdsa with identifiable aborts. In Proceed-
ings of the 2020 ACM SIGSAC Conference on Com-
puter and Communications Security, pages 1769–
1787. Association for Computing Machinery.
Canetti, R., Sarkar, P., and Wang, X. (2020b). Blazing Fast
OT for Three-Round UC OT Extension, pages 299–
327. Springer International Publishing.
Castagnos, G., Catalano, D., Laguillaumie, F., Savasta, F.,
and Tucker, I. (2020). Bandwidth-Efficient Threshold
EC-DSA, pages 266–296. Springer International Pub-
lishing.
Chuang, C., Hsu, I., and Lee, T. (2023). A two-party hi-
erarchical deterministic wallets in practice (extended
version). https://eprint.iacr.org/2023/714.
Das, P., Erwig, A., Faust, S., Loss, J., and Riahi, S.
(2023). Bip32-compatible threshold wallets. Cryp-
tology ePrint Archive.
Doerner, J., Kondi, Y., Lee, E., and Shelat, A. (2018). Se-
cure two-party threshold ecdsa from ecdsa assump-
tions. In 2018 IEEE Symposium on Security and Pri-
vacy (SP), pages 980–997.
Gennaro, R. and Goldfeder, S. (2018). Fast multiparty
threshold ecdsa with fast trustless setup. In Proceed-
ings of the 2018 ACM SIGSAC Conference on Com-
puter and Communications Security, pages 1179–
1194. Association for Computing Machinery.
Gennaro, R. and Goldfeder, S. (2020). One round thresh-
old ecdsa with identifiable abort. Cryptology ePrint
Archive.
Guo, C., Katz, J., Wang, X., and Yu, Y. (2020). Efficient and
secure multiparty computation from fixed-key block
ciphers. In 2020 IEEE Symposium on Security and
Privacy (SP), pages 825–841.
Gutoski, G. and Stebila, D. (2015). Hierarchical determin-
istic bitcoin wallets that tolerate key leakage. In Fi-
nancial Cryptography, pages 497–504.
Huang, Y., Katz, J., and Evans, D. (2012). Quid-pro-quo-
tocols: Strengthening semi-honest protocols with dual
execution. Proceedings - IEEE Symposium on Secu-
rity and Privacy, pages 272–284.
Lindell, Y. (2021). Fast secure two-party ecdsa signing.
Journal of Cryptology, 34.
Luis, A., Nicky, M., and Apostol, V. (2019). Threshold
schemes for cryptographic primitives.
M., N. (2005). Identifiers and test vectors for hmac-sha-
224, hmac-sha-256, hmac-sha-384, and hmac-sha-
512. https://datatracker.ietf.org/doc/html/rfc4231.
McQuoid, I., Rosulek, M., and Roy, L. (2021). Batching
Base Oblivious Transfers, pages 281–310. Springer
International Publishing.
Ostrovsky, R. and Yung, M. (1991). How to withstand mo-
bile virus attacks (extended abstract). In Proceedings
of the Tenth Annual ACM Symposium on Principles of
Distributed Computing, PODC ’91, pages 51–59. As-
sociation for Computing Machinery.
Pettit, M. (2021). Efficient Threshold-Optimal ECDSA,
pages 116–135. Springer-Verlag.
Wuille, P. (2013). Hierarchical deterministic wal-
lets. https://github.com/bitcoin/bips/blob/master/bip-
0032.mediawiki.
A Two-Party Hierarchical Deterministic Wallets in Practice
855