About
I am CY.
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]
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[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
Updating
- A Note on Various Forking Lemmas To-Read
- An Abstract Multi-Forking Lemma To-Read
- Random Oracle Model (ROM) Updating
- Fiat-Shamir (FS) Transformation Updating
- Discrete Logarithm, RSA, and the Structure of $\mathbb{Z}_p^*$
- $\Sigma$-Protocol Updating
Learning
Cryptography: An Introduction
Chapter 20 Provable Security: With Random OracleNigel Smart. Cryptography: An Introduction (Third Edition)
done reading todo
Practice
PortSwigger
Web Cache DeceptionPortSwigger Web Security Academy Learning Paths
done reading todo
CryptoHack
Symmetric Cryptographydone reading todo
Math Problem
Prime
Prime NumbersStudying prime numbers.
Papers
- [AKS04]
Patterns
Prime Number Theorem (PNT)
Primality Tests
- Primality Testingto-do
- Trial Divisionto-do
- Fermat Primality Testto-do
- Solovay-Strassen Testto-do
- Miller Testto-do
- Miller-Rabin Testto-do
- Lucas Probable Prime Teststo-do
- Baillie-PSW Testto-do
Primality Proving
- Pocklington Criterionto-do
- Pratt Certificatesto-do
- APR-CLto-do
- ECPPto-do
- AKSto-do
Tests for Special Forms
- Lucas-Lehmer Testto-do
- Pépin Testto-do
- Proth Testto-do
Conjecture
- Sophie Germain Primes Conjecture WORKING
- Twin Prime Conjecture to-do
- Dickson's Conjecture to-do
- Sophie-Germain Prime Density Conjecture WORKING
Others
Math NotesOther math notes.
Notes
Erdős Problem
There are 1217 problems in the database of which 529 (43%) have been solved.Erdős Problem Tracking classic open and solved problems inspired by Paul Erdős.
- Paul Erdős: Wikipedia (EN) / Wikipedia (ZH)
- Erdős number: Wikipedia (EN) / Wikipedia (ZH)
BLOG POSTS
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RECENT PAPERS
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OPEN -> SOLVED
- Coming soon.