ECDSA nonce bias caused by truncation

Generating the ECDSA nonce k samples a random number r and then truncates this randomness with a modular reduction mod n where n is the order of the elliptic curve. Meaning k = r mod n. The division used during the reduction estimates a factor q_e by dividing the upper two digits (a digit having e.g. a size of 8 byte) of r by the upper digit of n and then decrements q_e in a loop until it has the correct size. Observing the number of times q_e is decremented through a control-flow revealing side-channel reveals a bias in the most significant bits of k. Depending on the curve this is either a negligible bias or a significant bias large enough to reconstruct k with lattice reduction methods. For SECP160R1, e.g., we find a bias of 15 bits.

CVSS:3.1/AV:L/AC:H/PR:H/UI:N/S:U/C:H/I:N/A:N

通过差异性导致的信息暴露

wolfSSL 安全漏洞

wolfSSL（CyaSSL）是美国wolfSSL公司的一个针对嵌入式系统开发人员使用的小的、可移植的嵌入式SSL编程库。 wolfSSL 5.7.2 版本之前存在安全漏洞，该漏洞源于生成 ECDSA 时，使用的随机数不够随机。

N/A

N/A