RSA 加密为什么依赖‘大数难分解’？
Why does RSA encryption rely on 'large numbers are hard to factor'?
RSA 用两个大素数乘积作公钥，私钥相当于这两个因数。已知乘积却极难反推出因数（因数分解难），因此能公开加密、私密解密。
RSA uses the product of two large primes as the public key; the private key is effectively those two factors. Given the product, recovering the factors is computationally hard, enabling public encryption with private decryption.
难度 专业 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#密码 #数论
汉明码怎么在传输中自动纠错？
How do Hamming codes auto-correct errors in transmission?
它用若干校验位标记数据位的位置奇偶性；接收端重新计算校验，得到一个‘综合征’直接指出哪一位出错并可翻转修复。典型能纠正单个比特错误。
It uses parity check bits to mark positions; the receiver recomputes them to get a 'syndrome' that points exactly to the flipped bit, which is then corrected. It typically fixes a single-bit error.
难度 专业 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#纠错码 #可靠性
二维码为什么脏了一点还能扫出来？
Why can a QR code still scan when partly dirty?
二维码用了里德–所罗门等纠错码，把数据编码得能容忍一定比例的污损或遮挡而不丢失信息。这也是光盘划痕仍能读出的原理。
QR codes use Reed–Solomon error-correcting codes so data survives a certain fraction of dirt or occlusion without loss. The same idea lets scratched CDs still play.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#纠错码 #二维码