Codes from incidence matrices of some regular graphs

We examine the [Formula: see text]-ary linear codes with respect to Lee metric from incidence matrix of the Lee graph with vertex set [Formula: see text] and two vertices being adjacent if their Lee distance is one. All the main parameters of the codes are obtained as [Formula: see text] if [Formula: see text] is odd and [Formula: see text] if [Formula: see text] is even. We examine also the [Formula: see text]-ary linear codes with respect to Hamming metric from incidence matrices of Desargues graph, Pappus graph, Folkman graph and the main parameters of the codes are [Formula: see text], respectively. Any transitive subgroup of automorphism groups of these graphs can be used for full permutation decoding using the corresponding codes. All the above codes can be used for full error correction by permutation decoding.

New Insights to Key Derivation for Tamper-Evident Physical Unclonable Functions

Several publications presented tamper-evident Physical Unclonable Functions (PUFs) for secure storage of cryptographic keys and tamper-detection. Unfortunately, previously published PUF-based key derivation schemes do not sufficiently take into account the specifics of the underlying application, i.e., an attacker that tampers with the physical parameters of the PUF outside of an idealized noise error model. This is a notable extension of existing schemes for PUF key derivation, as they are typically concerned about helper data leakage, i.e., by how much the PUF’s entropy is diminished when gaining access to its helper data.To address the specifics of tamper-evident PUFs, we formalize the aspect of tamper-sensitivity, thereby providing a new tool to rate by how much an attacker is allowed to tamper with the PUF. This complements existing criteria such as effective number of secret bits for entropy and failure rate for reliability. As a result, it provides a fair comparison among different schemes and independent of the PUF implementation, as its unit is based on the noise standard deviation of the underlying PUF measurement. To overcome the limitations of previous schemes, we then propose an Error-Correcting Code (ECC) based on the Lee metric, i.e., a distance metric well-suited to describe the distance between q-ary symbols as output from an equidistant quantization, i.e., a higher-order alphabet PUF. This novel approach is required, as the underlying symbols’ bits are not i.i.d. which hinders applying previous state-of-the-art approaches. We present the concept for our scheme and demonstrate its feasibility based on an empirical PUF distribution. The benefits of our approach are an increase by over 21% in effective secret bit compared to previous approaches based on equidistant quantization. At the same time, we improve tamper-sensitivity compared to an equiprobable quantization while ensuring similar reliability and entropy. Hence, this work opens up a new direction of how to interpret the PUF output and details a practically relevant scheme outperforming all previous constructions.

r-Identifying codes in binary Hamming space, q-ary Lee space and incomplete hypercube

We study about monotonicity of [Formula: see text]-identifying codes in binary Hamming space, q-ary Lee space and incomplete hypercube. Also, we give the lower bounds for [Formula: see text] where [Formula: see text] is the smallest cardinality among all [Formula: see text]-identifying codes in [Formula: see text] with respect to the Lee metric. We prove the existence of [Formula: see text]-identifying code in an incomplete hypercube. Also, we give the construction techniques for [Formula: see text]-identifying codes in the incomplete hypercubes in Secs. 4.1 and 4.2. Using these techniques, we give the tables (see Tables 1–6) of upper bounds for [Formula: see text] where [Formula: see text] is the smallest cardinality among all [Formula: see text]-identifying codes in an incomplete hypercube with [Formula: see text] processors. Also, we give the exact values of [Formula: see text] for small values of [Formula: see text] and [Formula: see text] (see Sec. 4.3).