module: std
package: math/big
versions:
  - introduced: go1.5
    fixed: go1.5.3
description: |
    Int.Exp Montgomery mishandled carry propagation and produced an incorrect
    output, which makes it easier for attackers to obtain private RSA keys via
    unspecified vectors.

    This issue can affect RSA computations in crypto/rsa, which is used by
    crypto/tls. TLS servers on 32-bit systems could plausibly leak their RSA
    private key due to this issue. Other protocol implementations that create
    many RSA signatures could also be impacted in the same way.

    Specifically, incorrect results in one part of the RSA Chinese Remainder
    computation can cause the result to be incorrect in such a way that it leaks
    one of the primes. While RSA blinding should prevent an attacker from crafting
    specific inputs that trigger the bug, on 32-bit systems the bug can be expected
    to occur at random around one in 2^26 times. Thus collecting around 64 million
    signatures (of known data) from an affected server should be enough to extract
    the private key used.

    Note that on 64-bit systems, the frequency of the bug is so low
    (less than one in 2^50) that it would be very difficult to exploit.
cves:
  - CVE-2015-8618
credit: Nick Craig-Wood
symbols:
  - nat.expNNMontgomery
  - nat.montgomery
links:
    pr: https://go.dev/cl/18491
    commit: https://go.googlesource.com/go/+/1e066cad1ba23f4064545355b8737e4762dd6838
    context:
      - https://go.googlesource.com/go/+/4306352182bf94f86f0cfc6a8b0ed461cbf1d82c
      - https://go.dev/cl/17672
      - https://go.dev/issue/13515
      - https://groups.google.com/g/golang-announce/c/MEATuOi_ei4