Public Key Cryptography – PKC 2007

Volume 4450 of the series Lecture Notes in Computer Science pp 150-165

Knowledge-Binding Commitments with Applications in Time-Stamping

  • Ahto BuldasAffiliated withCybernetica AS, Akadeemia tee 21, 12618 TallinnTallinn University of Technology, Raja 15, 12618 TallinnUniversity of Tartu, Liivi 2, 50409 Tartu
  • , Sven LaurAffiliated withHelsinki University of Technology, Laboratory for Theoretical Computer Science, P.O.Box 5400, FI-02015 TKK


We prove in a non-black-box way that every bounded list and set commitment scheme is knowledge-binding. This is a new and rather strong security condition, which makes the security definitions for time-stamping much more natural compared to the previous definitions, which assume unpredictability of adversaries. As a direct consequence, list and set commitment schemes with partial opening property are sufficient for secure time-stamping if the number of elements has an explicit upper bound N. On the other hand, white-box reductions are in a sense strictly weaker than black-box reductions. Therefore, we also extend and generalize the previously known reductions. The corresponding new reductions are \(\Theta(\sqrt{N})\) times more efficient, which is important for global-scale time-stamping schemes where N is very large.