Figure 6.1: Singular values of the measurement matrix.
6.2.1 Measurement matrix evaluation
The functionality of the IC imposes dependencies in logic gate status. Thus, the
power vectors for the input vectors (i.e., the rows of the measurement matrix
A) are not necessarily independent. In this sections, we use the singular value
decomposition (SVD) to quantify the dependency of the rows of A.
A matrix with N independent rows has N non-zero singular values. The
sorted singular values of C499 and C880 circuits are shown in Figure 6.1 for a
measurement matrix with M = 6 × N measurements, where N is the number of
gates. On the figure the singular values for each circuit are normalized such that
the largest singular value is 1. The figure demonstrates that the singular values
decay rapidly; the 20-th singular value in both circuits are less than 10% (0.1).
68
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