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<p style='text-indent:20px;'>In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new <inline-formula><tex-math id="M1">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-cocycle <inline-formula><tex-math id="M2">\begin{document}$ \alpha_{\lambda} $\end{document}</tex-math></inline-formula> to twist the dihedral group algebra. Using the ambient space <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}^{\alpha_{\lambda}} D_{2n} $\end{document}</tex-math></inline-formula>, we then introduce a key exchange protocol and present an analysis of its security. Moreover, we explore the properties of the resulting twisted algebra <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{F}^{\alpha_{\lambda}}D_{2n} $\end{document}</tex-math></inline-formula>, exploiting them to enhance our key exchange protocol. We also introduce a probabilistic public-key scheme derived from our key-exchange protocol and obtain a key encapsulation mechanism (KEM) by applying a well-known generic transformation to our public-key scheme. Finally, we present a proof-of-concept implementation of the resulting key encapsulation mechanism.</p>

The applications that use blockchain are cryptocurrencies, decentralized finance applications, video games and many others. Most of these applications trust that the blockchain will prevent issues like fraud, thanks to the built-in cryptographic mechanisms provided by the data structure and the consensus protocol. However, blockchains suffers from what is called a 51% attack or majority attack, which is considered a high risk for the integrity of these blockchains, where if a miner, or a group of them, has more than half the computing capability of the network, it can rewrite the blockchain. Even though this attack is possible in theory, it is regarded as hard-achievable in practice, due to the assumption that, with enough active members, it is very complicated to have that much computing power; however, this assumption has not been studied with enough detail. In this work, a detailed characterization of the miners in the Bitcoin and Crypto Ethereum blockchains is presented, with the aim of proving the computing distribution assumption and to creating profiles that may allow the detection of anomalous behaviors and prevent 51% attacks. The results of the analysis show that, in the last years, there has been an increasing concentration of hash rate power in a very small set of miners, which generates a real risk for current blockchains. Also, that there is a pattern in mining among the main miners, which makes it possible to identify out-of-normal behavior.

In this paper, we will study the key enumeration problem, which is connected to the key recovery problem posed in the cold boot attack setting. In this setting, an attacker with physical access to a computer may obtain noisy data of a cryptographic secret key of a cryptographic scheme from main memory via this data remanence attack. Therefore, the attacker would need a key-recovery algorithm to reconstruct the secret key from its noisy version. We will first describe this attack setting and then pose the problem of key recovery in a general way and establish a connection between the key recovery problem and the key enumeration problem. The latter problem has already been studied in the side-channel attack literature, where, for example, the attacker might procure scoring information for each byte of an Advanced Encryption Standard (AES) key from a side-channel attack and then want to efficiently enumerate and test a large number of complete 16-byte candidates until the correct key is found. After establishing such a connection between the key recovery problem and the key enumeration problem, we will present a comprehensive review of the most outstanding key enumeration algorithms to tackle the latter problem, for example, an optimal key enumeration algorithm (OKEA) and several nonoptimal key enumeration algorithms. Also, we will propose variants to some of them and make a comparison of them, highlighting their strengths and weaknesses.

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