← ToolBox / 校验和碰撞概率

#️⃣ Checksum Collision Probability

Estimate the undetected-error probability from checksum bit width and data volume; suitable for random errors only, not adversarial tampering.

校验位宽 bits

尝试次数

待校验数据 bits

n 位校验和的随机漏检概率 ≈ 2⁻ⁿ
累计 ≈ 1 − (1 − 2⁻ⁿ)^N

仅适用于随机错误，不能防蓄意篡改。

📚 深度解析：校验和碰撞概率

示例：16 位校验和、10^6 包

随机错误漏检率约 1/65536 量级，但蓄意攻击者仍可控构造碰撞，故仅用于非安全场景。

Item	Formula / Rule	Source / Standard
Undetected error rate	A k-bit checksum misses about 2^−k of random errors	Peterson & Brown, Cyclic Codes for Error Detection, 1961
Single-bit errors	When the generator polynomial has (x + 1) as a factor, every single-bit error is detected	ISO/IEC 3309 HDLC frame structure and FCS
Burst errors	Bursts of length ≤ k are always detected; longer bursts slip through at most 2^−k	ITU-T X.25 §2.2.7.4 Frame Check Sequence