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GCKSign: Simple and efficient signatures from generalized compact knapsack problems.

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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.

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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.