What is a side-channel attack, and how does Simple Power Analysis (SPA) work against RSA?

A side-channel attack extracts secret keys by observing physical properties (power consumption, timing, radiation) rather than attacking the math.

How SPA works against RSA:

RSA operations involve repeated squarings and multiplications. The secret key is a binary number (e.g., 1001101111):

• For a "1" bit → perform both a multiplication AND a squaring
• For a "0" bit → perform only a squaring

These two operations consume different amounts of electrical power. By measuring the power consumption over time with an oscilloscope, an attacker can read the key bit by bit:

• High power spike = multiplication + squaring = key bit "1"
• Low power spike = squaring only = key bit "0"

Types of side-channel attacks:

• SPA (Simple Power Analysis) — directly observing power patterns
• DPA (Differential Power Analysis) — statistical analysis of many power traces
• Timing attacks — measuring how long operations take
• Electromagnetic emanation — capturing EM radiation from chips
• Video-based cryptanalysis — reading keys from power LED flicker captured by cameras

Countermeasure: Use constant-time, constant-power implementations, or add random noise to operations.