Research
MBDL as a Hub
The problem: MBDL as a HubIn a follow-up work, give reductions from MBDL that improve security of the following: (1) Bellare-Neven multi-signature, (2) Abe, Ohkubo, Suzuki 1-out-of-n (ring/group) signatures, and (3) Schnorr-based threshold signatures.
Papers
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[BN06]
Multi-Signatures in the Plain Public-Key Model and a General Forking Lemma
Mihir Bellare and Gregory Neven. ACM CCS 2006. -
[AOS02]
1-out-of-n Signatures from a Variety of Keys
Masayuki Abe, Miyako Ohkubo, and Koutarou Suzuki. ASIACRYPT 2002. -
[SS01]
Provably Secure Distributed Schnorr Signatures and a $(t, n)$ Threshold Scheme for Implicit Certificates
Douglas R. Stinson and Reto Strobl. ACISP 2001.
Notes to-do
Square-Root Barrier
The problem: Square-Root BarrierThe “square-root barrier” is the open problem of obtaining tight (no √-loss) security reductions for Fiat–Shamir signatures (e.g., Schnorr/GQ). Standard rewinding/forking proofs often lose a √ factor because extraction needs two accepting transcripts.
Papers
- [Sho97]
-
[BNPS03]
The One-More-RSA-Inversion Problems and the Security of Chaum's Blind Signature Scheme
Mihir Bellare, Chanathip Namprempre, David Pointcheval, and Michael Semanko. Journal of Cryptology, 2003.
The Power of RSA Inversion Oracles and the Security of Chaum's RSA-Based Blind Signature Scheme
[The preliminary version] Financial Cryptography 01, Lecture Notes in Computer Science Vol. 2339, P. Syverson ed, Springer-Verlag, 2001. -
[BP02]
GQ and Schnorr Identification Schemes: Proofs of Security against Impersonation under Active and Concurrent Attacks
Mihir Bellare and Adriana Palacio. CRYPTO 2002. -
[BD20]
The Multi-Base Discrete Logarithm Problem: Tight Reductions and Non-Rewinding Proofs for Schnorr Identification and Signature
Mihir Bellare and Wei Dai. INDOCRYPT 2020. -
[BFP21]
The One-More Discrete Logarithm Assumption in the Generic Group Model
Balthazar Bauer, Georg Fuchsbauer, and Antoine Plouviez. ASIACRYPT 2021. -
[RS24]
Tighter Security for Schnorr Identification and Signature: A High-Moment Forking Lemma for $\Sigma$-Protocols
Lior Rotem and Gil Segev. Journal of Cryptology, July 2024. -
[HM25]
Tight Bounds on Uniform-Challenge Reductions from Sigma Protocols via Hitting Games
Iftach Haitner and Nikolaos Makriyannis. EUROCRYPT 2026
Notes to-do
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Forking Lemma
working
- A Note on Various Forking Lemmas to-read
- An Abstract Multi-Forking Lemma to-read
- Random Oracle Model (ROM) working
- Fiat-Shamir (FS) Transformation working
- Discrete Logarithm, RSA, and the Structure of $\mathbb{Z}_p^*$
- $\Sigma$-Protocol working