Key-Reuse Vulnerability of Phase-Keyed Fourier-Curve Modulation: Relation Leakage and Key-Refresh Cost on Coded Links
Researchers show key reuse in phase-keyed Fourier-curve modulation leaks the key via harmonic relation moments, forcing costly refresh.
A phase-keyed Fourier-curve constellation reuses one key across harmonically coupled tones, and integer relations among harmonic indices create data-cancelling mixed moments that reveal key characters. For consecutive harmonics, third-order moments recover relative phases and a nonzero fourth-order moment completes the key up to cyclic relabeling, without searching the key space. On a regular (3,6) LDPC link, one key per 168-symbol codeword leaves an eavesdropper block error rate below 0.04 at the middle noise level, meeting a 0.1 compromise criterion in 11 of 12 points. Maintaining a 95% lower confidence bound above 0.9 block error for a 2^128 key grid requires at least 1.52 fresh key bits per information bit.
- Consecutive harmonics leak relative phases through third-order moments.
- A fourth-order moment recovers the key up to cyclic relabeling.
- One key per 168-symbol LDPC codeword yields block error below 0.04.
- Safe refresh costs at least 1.52 fresh key bits per information bit.
From the original article
1 min read at arxiv.orgThe security of keyed modulation is often argued from the key-space size and the error rate of a key-less receiver. This evidence fails when the key is reused and the waveform is harmonically coupled. For a phase-keyed Fourier-curve constellation, whose $k$ tones share one data parameter, integer relations among the harmonic indices yield data-cancelling mixed moments of the received tones that expose key characters.
By Bin Han · arxiv.org
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