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GCKSign: Simple and efficient signatures from generalized compact knapsack problems
Joo Woo1, Kwangsu Lee2, Jong Hwan Park3
1Graduate School of Information Security, Korea University, Seoul, South Korea.
Plos One
|September 23, 2024
Summary
This study introduces GCKSign, a more efficient lattice-based digital signature scheme. GCKSign significantly reduces public key and signature sizes compared to previous methods by removing the witness indistinguishability property.
Area of Science:
- Cryptography
- Computer Science
- Number Theory
Background:
- Lattice-based cryptography offers post-quantum security.
- Lyubashevsky's 2009 scheme used witness indistinguishability (WI), causing inefficiency.
- Existing schemes face challenges with public key and signature size.
Purpose of the Study:
- To develop a more efficient lattice-based signature scheme.
- To overcome the efficiency limitations of witness indistinguishability.
- To introduce a new lattice-based security assumption.
Main Methods:
- Introduced the target-modified one-wayness (GCK-TMO) problem for Module GCK functions.
- Reduced the new GCK-TMO problem to established lattice problems.
- Proposed the GCKSign scheme based on the Module GCK-TMO problem.
- Analyzed security in the random oracle model.
Main Results:
- GCKSign achieves efficiency gains by eliminating the WI property.
- Signatures are 3.4 times shorter than Lyubashevsky's scheme.
- Public keys are 2.4 times shorter at equivalent security levels.
Conclusions:
- GCKSign offers a practical and efficient alternative for lattice-based digital signatures.
- The new GCK-TMO assumption provides a foundation for secure and efficient cryptographic primitives.
- This work advances the development of smaller and faster lattice-based cryptographic solutions.
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