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Towards a Cryptanalysis of Spectral-Phase Encoded Optical CDMA with Phase-Scrambling

Report ID:
October 2006
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Optical CDMA (OCDMA) is a particularly attractive alternative to traditional digital encryption because it has the potential to perform encryption at ultra-high data rates by initializing passive optical components (e.g. phase masks, delay lines) according to a secret key that needs only occasional updates. To be a viable alternative to digital encryption, OCDMA systems should maintain data confidentiality even when these optical components are reconfigured (i: e: the key is refreshed) at rates much slower than aggregate system data rates. We focus on spectral-phase-encoded OCDMA systems using phase-scrambling, which have emerged as the leading proposal for providing data confidentiality at the physical layer. Typical OCDMA schemes require some orthogonality between codewords and are therefore restricted to use codes with low cardinality.

These schemes are therefore vulnerable to brute force searches by an eavesdropper who cycles through all possible codewords in an effort to find one that results an ungarbled datastream. On the other hand, a spectral-phase scrambling scheme offers a keyspace that grows exponentially with the number of frequency bins used, so that brute-force searches can be made infeasible.

We assume that the secret key used in the system is the setting of
the phase-scrambler, and analyze this system using the assumptions of cryptanalysis. In particular, we explore known plaintexts attacks in which an eavesdropper obtains the encryption of some set of known messages, and uses this information to learn the secret key. Our first contribution is to show circumstances in which confidentiality is determined by the parallelism (i: e: the number of users) in the system, rather than by the number of frequency bins used for encoding. Our next contribution is to show that even when some systems are highly parallelized (i: e: have a large number of users), an eavesdropper can still learn the key with high probability after only two bit intervals. Our results thus far suggest that to maintain confidentiality when the secret key is the phase-scrambler setting, components should be tuned at rates comparable to the system data rates.

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