Partial Key Exposure Attacks

發表於 2026-02-06 | 更新於 2026-02-06 | RSA partial-key-exposure

Partial Key Exposure Attacks（部分私鑰洩漏攻擊） 描述一種「私鑰只部分洩漏」的情境：攻擊者僅取得 private key 的部分位元（例如 MSB/LSB、某段連續 bits、或分散的若干 bits），仍可能藉由數論結構與演算法技巧重建完整私鑰，進而造成系統的 total break。

Partial Exposure of the MSBs of the RSA Decryption Exponent

Partial Exposure of the MSBs of the RSA Decryption Exponent

Partial Exposure of the some bits of the RSA Prime Factors

Partial Exposure of the some bits of the RSA Prime Factors

Partial Exposure of the LSBs of the RSA Decryption Exponent

Partial Exposure of the LSBs of the RSA Decryption Exponent

References

• Nigel P. Smart, Cryptography: An Introduction (3rd ed.), Chapter 17. PDF