Founder Eben Upton has offered an explanation as to why the Raspberry Pi is immune to both Spectre and Meltdown. The short version is that the Pi uses ARM1176, Cortex-A7, and Cortex-A53 cores, which utilize an in-order, not out-of-order, architecture. This is actually a nice summary of how Spectre, Meltdown, and CPUs work.
Both vulnerabilities exploit performance features (caching and speculative execution) common to many modern processors to leak data via a so-called side-channel attack. Happily, the Raspberry Pi isn’t susceptible to these vulnerabilities, because of the particular ARM cores that we use.
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Source: [H]ardOCP – Why Raspberry Pi Isn’t Vulnerable to Spectre or Meltdown