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 qe 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 qe 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.
{
"cna_assigner": "wolfSSL",
"cwe_ids": [
"CWE-203"
],
"osv_generated_from": "https://github.com/CVEProject/cvelistV5/tree/main/cves/2024/1xxx/CVE-2024-1544.json"
}{
"cpe": "cpe:2.3:a:wolfssl:wolfssl:*:*:*:*:*:*:*:*",
"source": [
"AFFECTED_FIELD",
"CPE_RANGE",
"REFERENCES"
],
"extracted_events": [
{
"introduced": "0"
},
{
"last_affected": "5.6.4"
},
{
"fixed": "5.7.2"
}
]
}