Theory and Applications of Sequentially Threshold Public-Key Cryptography: Practical Private Key Safeguarding and Secure Use for Individual Users

Motivated by the needs of power distribution as well as private key protection, the theory and implementation techniques of threshold public-key cryptography (PKC) have been being developed for a long time. However, researches in this field mainly focus on the needs and constraints in distributed environments which consist of nodes with computing capabilities and connected via peer-to-peer and broadcasting communication channels. The resulting schemes are theoretically helpful for private key security but inconvenient for individual users as their implementation requires distributed computing and networking system with broadcasting channels. To address the private key security issue of PKC schemes for individual users, this paper proposes the concept and general construction of sequentially threshold PKC under a communication model consisting of a computing device and several offline storages where broadcasting channels are not required. To illustrate the new paradigm, we design and realize a sequentially threshold Schnorr signature scheme <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">STSS</monospace>. The security proofs for <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">STSS</monospace> indicate its effectiveness of achieving unforeability under traditional attacks as well as security incidents caused by human faults and system failures. The experiments on FIPS recommended curves P-256, P-384, and P-521 show that <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">STSS</monospace> is comparable with the original Schnorr scheme in terms of time consumed for generating a signature. The construction of sequentially threshold ElGamal decrtyption scheme is also presented. Finally, we illustrate the application of <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">STSS</monospace> in the Blockchain ecosystem.