CVE-2016-2849 in Botan
Summary
by MITRE
Botan before 1.10.13 and 1.11.x before 1.11.29 does not use a constant-time algorithm to perform a modular inverse on the signature nonce k, which might allow remote attackers to obtain ECDSA secret keys via a timing side-channel attack.
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Analysis
by VulDB Data Team • 08/19/2022
The vulnerability identified as CVE-2016-2849 affects the Botan cryptographic library, specifically versions prior to 1.10.13 and 1.11.x before 1.11.29. This flaw resides in the implementation of elliptic curve digital signature algorithm (ECDSA) operations where the library fails to employ constant-time algorithms for computing modular inverses during signature generation. The issue stems from the signature nonce k being processed using variable-time arithmetic operations that expose timing information to potential attackers. This vulnerability represents a significant security concern as it directly impacts the confidentiality of elliptic curve private keys used in ECDSA signatures.
The technical implementation flaw manifests in how the library handles the modular inverse computation required for ECDSA signature verification. When generating ECDSA signatures, the system must compute the modular inverse of the nonce k modulo the order of the elliptic curve group. In vulnerable versions of Botan, this computation does not follow constant-time execution patterns, meaning the time required to complete the operation varies based on the input values. Attackers can exploit this timing variation through side-channel analysis to gradually reconstruct the private key components. The vulnerability is classified as a timing side-channel attack that violates fundamental security principles for cryptographic implementations. This issue aligns with CWE-325 which addresses missing cryptographic steps and CWE-327 which covers use of broken or weak cryptographic algorithms.
The operational impact of this vulnerability extends beyond simple cryptographic weakness to potentially compromise entire security infrastructures relying on Botan for ECDSA operations. Remote attackers who can observe timing variations in signature generation processes can perform statistical analysis over multiple signature requests to deduce the private key through mathematical reconstruction techniques. This attack vector is particularly dangerous because it requires no direct access to the signing system or its memory, only the ability to measure execution times of signature operations. The vulnerability affects any application using Botan's ECDSA implementation for digital signatures, including TLS implementations, certificate authorities, and cryptographic protocols requiring ECDSA verification. The attack can be executed against systems using weak elliptic curves or those with insufficient entropy in their nonce generation, making the exploitation more feasible.
Mitigation strategies for CVE-2016-2849 require immediate upgrading of Botan libraries to versions 1.10.13 or 1.11.29 and later, which implement constant-time modular inverse algorithms. Organizations should also consider implementing additional protections such as randomizing the timing of cryptographic operations, using hardware security modules for signature generation, or employing alternative cryptographic libraries that have been verified for constant-time operations. Security teams must conduct thorough audits of all systems using vulnerable Botan versions and implement monitoring for potential timing side-channel attacks. The fix addresses the underlying algorithmic weakness by ensuring that all modular inverse computations execute in constant time regardless of input values, thereby eliminating the timing information that attackers could exploit. This remediation aligns with best practices outlined in NIST SP 800-57 and follows the ATT&CK technique T1005 for data from local system and T1046 for network service scanning that could be used to detect vulnerable systems. Organizations should also consider implementing cryptographic agility frameworks to ensure future resilience against similar timing-based attacks and maintain updated cryptographic libraries across all infrastructure components.