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J.H. Conway suggested to use norm-compatible polynomialswhen constructing extension fields in order to get finite field embeddings, which are computationally easy to handle. Analogous to norm-compatibility for the multiplicative group of zffq we exhibit the notion of trace-compatibility for its additive group. By this we get computationally simple embeddings in the case of normal basis representations of finite fields. We give an algorithm for computing tracecompatible polynomials and count the number of distinct compatible polynomials of a fixed degree of both kinds.

The Internet of Things (IoT) relies on sensor devices to measure real-world phenomena in order to provide IoT services. The sensor readings are shared with multiple entities, such as IoT services, other IoT devices or other third parties. The collected data may be sensitive and include personal information.To protect the privacy of the users, the data needs to be protected through an encryption algorithm. For sharing cryptographic cipher-texts with a group of users Attribute-Based Encryption (ABE) is well suited, as it does not require to create group keys. However, the creation of ABE cipher-texts is slow when executed on resource constraint devices, such as IoT sensors. In this paper, we present a modification of an ABE scheme, which not only allows to encrypt data efficiently using ABE, but also reduces the size of the cipher-text, that must be transmitted by the sensor. We also show how our modification can be used to realise an instantaneous key revocation mechanism.

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