CVE-2015-8618 in Google
Summary
by MITRE
The Int.Exp Montgomery code in the math/big library in Go 1.5.x before 1.5.3 mishandles carry propagation and produces incorrect output, which makes it easier for attackers to obtain private RSA keys via unspecified vectors.
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Analysis
by VulDB Data Team • 07/06/2022
The vulnerability identified as CVE-2015-8618 resides within the math/big library of the Go programming language, specifically affecting versions 1.5.x prior to 1.5.3. This issue impacts the implementation of Montgomery multiplication, a critical algorithm used in cryptographic operations including RSA key generation and signature verification. The flaw manifests in the handling of carry propagation during arithmetic operations, which is fundamental to the correctness of modular exponentiation calculations that underpin RSA cryptography.
The technical nature of this vulnerability stems from an error in the internal implementation of the Montgomery multiplication algorithm within Go's big integer library. When performing modular arithmetic operations, the algorithm must correctly manage carries that propagate through multiple limbs or word-sized chunks of the large integer representation. The improper carry handling causes the algorithm to produce incorrect intermediate results during computation, which can lead to miscalculations in the final cryptographic output. This type of flaw falls under the CWE-682 category of "Incorrect Calculation" and represents a significant weakness in the mathematical foundation upon which cryptographic security relies.
The operational impact of CVE-2015-8618 is severe and directly threatens the security of RSA-based cryptographic systems that depend on Go's math/big library. Attackers can exploit this vulnerability to recover private RSA keys through unspecified vectors that leverage the incorrect mathematical results produced by the flawed Montgomery multiplication implementation. The vulnerability creates a path for adversaries to potentially compromise encrypted communications, digital signatures, and authentication mechanisms that rely on RSA cryptography. This aligns with ATT&CK technique T1552.004 for "Credentials from Password Stores" and T1003.002 for "OS Credential Dumping" when considering the potential for private key extraction and credential compromise.
The vulnerability's exploitation potential is particularly concerning because it affects the fundamental arithmetic operations that cryptographic libraries depend upon for security. When cryptographic software relies on incorrect mathematical operations, it can lead to key recovery attacks that bypass traditional security measures. The issue demonstrates how low-level mathematical errors in cryptographic implementations can have far-reaching consequences for security systems. Organizations using Go applications with RSA cryptography were particularly vulnerable, as the flaw could enable attackers to perform successful cryptanalysis against RSA-encrypted data or to forge digital signatures. The vulnerability underscores the critical importance of rigorous mathematical correctness in cryptographic implementations and the need for thorough testing of mathematical algorithms in security-sensitive contexts.