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In this article, we present implementations for Addition, Rotation, and eXclusive-or (ARX)-based block ciphers, including LEA and HIGHT, on IoT devices, including 8-bit AVR, 16-bit MSP, 32-bit ARM, and 32-bit ARM-NEON processors. We optimized 32-/8-bitwise ARX operations for LEA and HIGHT block ciphers by considering variations in word size, the number of general purpose registers, and the instruction set of the target IoT devices. Finally, we achieved the most compact implementations of LEA and HIGHT block ciphers. The implementations were fairly evaluated through the Fair Evaluation of Lightweight Cryptographic Systems framework, and implementations won the competitions in the first and the second rounds.

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Abstract. For a finite group G to be used in the MOR public key cryptosystem, it is necessary that the discrete logarithm problem(DLP) over the inner automorphism group Inn(G) of G must be computationally hard to solve. In this paper, under the assumption that the special conjugacy problem of G is easy, we show that the complexity of the MOR system over G is about log |G| times larger than that of DLP over G in a generic sense. We also introduce a group-theoretic method, called the group extension, to analyze the MOR cryptosystem. When G is considered as a group extension of H by a simple abelian group, we show that DLP over Inn(G) can be 'reduced' to DLP over Inn(H). On the other hand, we show that the reduction from DLP over Inn(G) to DLP over G is also possible for some groups. For example, when G is a nilpotent group, we obtain such a reduction by the central commutator attack.

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