SPA/DPA

SPA/DPA

Simple Power Analysis (SPA) and Differential Power Analysis (DPA) are side-channel attacks that extract secret cryptographic keys by analyzing the power consumption patterns of a smart card chip during cryptographic operations. First published by Paul Kocher in 1999, these techniques revolutionized the understanding of physical security in embedded devices and directly shaped modern smart card chip design.

Simple Power Analysis (SPA)

SPA involves directly observing the power consumption trace of a single cryptographic operation. Because different instructions (multiply vs. square in RSA, branch vs. no-branch in DES) consume measurably different amounts of power, an attacker can visually identify which operation the processor is executing at each clock cycle.

For example, in a naive RSARSACryptographyPublic-key algorithm for smart card signatures and key exchange.Click to view → implementation, a "square" operation has a distinct power signature from a "multiply" operation. By reading the sequence of squares and multiplies from one power trace, the attacker can reconstruct the private exponent bit by bit.

Differential Power Analysis (DPA)

DPA is a statistical technique that overcomes noise and measurement limitations by collecting thousands of power traces across multiple operations with different inputs. The attacker formulates hypotheses about key bits, predicts the intermediate computation values, and correlates predicted values with observed power consumption using statistical tests (difference of means, correlation coefficient, or mutual information).

DPA is more powerful than SPA because:

• It works even when individual traces are too noisy to interpret visually
• It can extract keys from implementations with basic SPA countermeasures
• It scales to any symmetric or asymmetric algorithm (AES, 3DES, ECC)

Countermeasures in Modern Smart Cards

Smart card chip manufacturers implement multiple layers of DPA countermeasures:

These countermeasures are mandatory for Common Criteria certification — EAL 4+ and above requires demonstrated resistance to DPA in the JIL vulnerability assessment.