INTRAS Data Scrambling

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In the previous section, the general infrastructure and several approaches for generating and establishing common keys at various nodes in a secure manner have been described. The next strategy involves utilizing these keys in some symmetric encryption scheme [6]. To this end, we propose a symmetric data scrambling method that operates at the signal-sample level. The method is referred to as INTRAS [33, 34], being effectively a combination of interpolation and random sampling, which is inspired by

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references 43 and 44. The idea is to modify the signal after sampling, but before binary encoding. 16.5.3.1 Bit-Level Versus Signal-Level Cryptography

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The proposed method is suitable for input data at the signal-level (nonbinary) form, which is typical of the raw data transmitted in a BSN. The scheme is meant to tolerate small key variations (a problem for conventional encryption: even a single-bit key error, by design, results in nonsense output), as well as to deliver a low-complexity implementation. However, the cost to be paid is a possibly imperfect recovery, due to interpolation diffusion errors with an imperfect key sequence. It will be seen that in the presence of key variations, the resulting distortions are similar to gradual degradations found in lossy compression algorithms, as opposed to the all-or-none abrupt recovery failure exhibited by conventional encryption. 16.5.3.2 INTRAS Structure

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The general high-level structure of an INTRAS scrambler is shown in Figure 16.14, with input sequence x[n]. At each instant n, the resampling block simply resamples the interpolated signal xI (t) using a delay d[n] to produce the scrambled output xd [n]. Security here is obtained from the fact that by properly designing the interpolating lter, the input cannot be recovered from the scrambled output xd [n], without knowledge of the delay sequence d[n]. Moreover, when d[n] is a random sequence, as will be described next, the operation corresponds to random sampling. In a BSN context, the available (binary) encryption key ksession is used to generate a set of sampling instants d[n], by multilevel symbol-coding of ksession [45]. This set of sampling instants is then used to resample the interpolated data sequence. Note that, when properly generated, ksession is a random key and that the derived d[n] inherits this randomness. In other words, the resampling process corresponds effectively to random sampling of the original data sequence. Without knowledge of the key sequence, the unauthorized recovery of the original data sequence (e.g., by brute-force attack), from the resampled signal is computationally impractical. By contrast, with knowledge of d[n], the recovery of the original data is ef ciently performed; in some cases, an iterative solution is possible. Therefore, the proposed scheme satis es the main characteristics of a practical cryptographic system. More importantly, it not only requires less computational resources for implementation, but also is more robust to small mismatching of the encryption and decryption keys, which is often the case in biometrics systems.

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x[n]

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Interpolating x I (t) Filter

Resample x I (t) with delay d[n]

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x d [n]

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Figure 16.14. Interpolation and random sampling (INTRAS) structure.

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INTRAS with Linear Interpolators

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While Figure 16.14 shows an intermediate interpolated analog signal, xI (t), this is more or less a convenient abstraction only. It turns out that, depending on the lter used and the method of resampling, we can in fact bypass the continuous-time processing completely. First, the window size or memory length M needs to be selected, determining the range of time instants of over which the resampling can occur. For a causal de nition, we require that the window span only the previous data symbols. Then, the current output symbol is obtained as a linear combination of the previous symbols. Consider a simple linear interpolator with M = 1, so that the window size is two symbols, consisting of the current symbol and one previous symbol. Then the resampled signal xd [n] can be obtained in discrete-time form as xd [n] = a0 [n] x[n] + a1 [n] x[n 1] = d[n] x[n] + (1 d[n]) x[n 1], (16.18) where 0 d[n] 1. The rationale for this de nition is illustrated in Figure 16.15. We note that this is a causal de nition. When d = 0, the output is the previous symbol. When d = 1, it is the current symbol. And for 0 < d < 1, the lter interpolates between these values. This is precisely what a linear interpolator does, but implemented entirely in discrete-time. The iterative (16.18) needs initialization to be complete: A virtual pre-symbol can be de ned with an arbitrary value x[ 1] = A. Also, observe that computing xd [n] actually corresponds to computing a convex combination of two consecutive symbols x[n] and x[n 1]; that is, weighting coef cients a0 and a1 satisfy a0 + a1 = 1, a0 0, a1 0 (16.19) (16.20)

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