A generalization of the original Diffie-Hellman key exchange in $(\mathbb Z$∕$p\mathbb Z)$^* found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 5 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.

We consider a key-exchange protocol based on matrices over a tropical semiring which was recently proposed in [2]. We show that a particular private parameter of that protocol can be recovered with a simple binary search, rendering it insecure.

Because of the theoretical challenges posed by the Efficient Market Hypothesis with respect to technical analysis, the effectiveness of technical indicators in high-frequency trading remains inadequately explored, particularly at the minute-level frequency, where the effects of the microstructure of the market dominate. This study evaluates the integration of traditional technical indicators with Random Forest regression models using minute-level SPY data, analyzing 13 distinct model configurations. Our empirical results reveal a stark contrast between in-sample and out-of-sample performance, with $R^2$ values deteriorating from 0.749–0.812 during training to negative values in testing. A feature importance analysis demonstrates that primary price-based features dominate the predictions made by the model, accounting for over 60% of the importance, while established technical indicators, such as RSI and Bollinger Bands, account for only 14–15%. Although the indicator-enhanced models achieved superior risk-adjusted metrics, with Rachev ratios between 0.919 and 0.961, they consistently underperformed a simple buy-and-hold strategy, generating returns ranging from −2.4% to −3.9%. These findings challenge conventional assumptions about the usefulness of technical indicators in algorithmic trading, suggesting that in high-frequency contexts, they may be more relevant to risk management rather than to predicting returns. For practitioners and researchers, our findings indicate that successful high-frequency trading strategies should focus on adaptive feature selection and regime-specific modeling rather than relying on traditional technical indicators, as well as indicating the critical importance of robust out-of-sample testing in the development of a model.

A generalization of the original Diffie-Hellman key exchange in F/sub p/ found a new depth when Miller (1986) and Koblitz (1987) suggested that such a protocol could be used with the group over an elliptic curve. In the present article, we extend such a generalization to the setting of a semigroup action (G-action) on a finite set. We define this extended protocol, show how it is related to the general Diffie-Hellman key exchange and give some examples. The interesting thing is that every action by an abelian semigroup gives rise to a Diffie-Hellman key exchange. With an additional assumption it is also possible to extend the ElGamal protocol.

Recently, Shpilrain and Sosnovski proposed a hash function based on composition of affine maps. In this paper, we show that this hash function with its proposed parameters is not weak collision resistant, for plaintexts of size at least 1.9MB (about {2^{24}} bits). Our approach is to reduce the preimage problem to a (very) high density instance of the Random Modular Subset Sum Problem, for which we give an algorithm capable of solving instances of the resulting size. Specifically, given plaintexts of about 1.9MB, we were able to produce other plaintexts of the same size with the same hash value in about 13 hours each, on average.

In several recent works of D. Kahrobaei, C. Koupparis, and V. Shpilrain, public-key protocols have been proposed which depend on the difficulty of computing discrete logarithms in matrix rings over group rings. In particular, the specific ring of 3×3 matrices over