Exploring the Intersection of Lattice Attacks and Blockchain Technology: A Heuristic Approach Using TPM2.0 ECDSA to Ascertain and Approach the Boundary

Lattice attacks can compromise the security of encryption algorithms used in blockchain networks, allowing attackers to tamper with transaction records, steal private keys, and execute other forms of attacks. With symmetric encryption, both parties can encrypt and decrypt messages using the same key. Lattice attacks on digital signature algorithms (ECDSA) involve forming a basis and setting a target vector from signatures, then solving the closest vector problem (CVP) or shortest vector problem (SVP) in the generated lattice to obtain the private key. Prior research focused on obtaining leakage information from the signature’s random nonce to facilitate a CVP or SVP solution. This study establishes a clear boundary for a successful ECDSA attack and introduces a “double basis” lattice version that expands the boundary or reduces the necessary signatures by nearly half with the same lattice rank. To approach the boundary, a heuristic strategy is employed to shift the target vector in different directions with a feasible step size, using tests on the Trusted Platform Module (TPM) 2.0 ECDSA. The distance from the closest moved target vector to the boundary is reduced by a ratio of 424 to 179 to the minimal length of orthogonal vectors in the formed basis. Experimental results show that moving attempts in two directions with the original basis and 84 signatures take approximately 247.7 s on the experiment computer.