基於隱藏數問題在(EC)DSA 上的部份洩漏攻擊

Abstract

1996 年，Boneh 和Venkatesan 提出隱藏數問題，並在位元安全性和隱藏數問題之間建立聯繫。隱藏數問題最初用於證明一些密碼架構的位安全性。然而，隱藏數問題也被用於攻擊數位簽章演算法。在特定情況下，我們可以藉助晶格縮減、最接近向量問題演算法和特定假設來恢復私鑰。本文旨在實現基於隱藏數問題在特定密鑰交換協定、數位簽章演算法(DSA) 和橢圓曲線數位簽章算法（ECDSA）上的晶格攻擊。

In 1996, Boneh and Venkatesan introduced the Hidden Number Problem (HNP) and built the connection between bit security and HNP. The HNP was originally used in the proof of the bit security of several cryptographic schemes. Nevertheless, the HNP was also applied to break the certain digital signature schemes. In the particular situation, we can recover the private key with help of the lattice reduction, closest vector problem (CVP) algorithms, and specific assumptions. In this paper, we aim to implement the lattice attack based on HNP against the certain key exchange protocol, digital signature algorithm (DSA), and elliptic curve digital signature algorithm (ECDSA).