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Strategies and their evaluations play important roles in speeding up the computation of large smooth-degree isogenies. The concept of optimal strategies for such computation was introduced by De Feo et al., and virtually all implementations of isogeny-based protocols have adopted this approach, which is provably optimal for single-core platforms. In spite of its inherent sequential nature, several recent works have studied ways of speeding up this isogeny computation by exploiting the rich parallelism available in vectorized and multi-core platforms. One obstacle to taking full advantage of this parallelism, however, is that De Feo et al.’s strategies are not necessarily optimal in multi-core environments. To illustrate how the speed of vectorized and parallel isogeny computation can be improved at the strategylevel, we present two novel software implementations that utilize a state-of-the-art evaluation technique, called precedence-constrained scheduling (PCS), presented by Phalakarn et al., with our proposed strategies crafted for these environments. Our first implementation relies only on the parallelism provided by multi-core processors. The second implementation targets multi-core processors supporting the latest generation of the Intel’s Advanced Vector eXtensions (AVX) technology, commonly known as AVX-512IFMA instructions. To better handle the computational concurrency associated with PCS, we equip both implementations with extensive synchronization techniques. Our first implementation outperforms the implementation of Cervantes-Vázquez et al. by yielding up to 14.36% reduction in the execution time, when targeting platforms with two- to four-core processors. Our second implementation, equipped with four cores, achieves up to 34.05% reduction in the execution time compared to the single-core implementation of Cheng et al. of CHES 2022.

Classical cryptographic schemes in use today are based on the difficulty of certain number theoretic problems. Security is guaranteed by the fact that the computational work required to break the core mechanisms of these schemes on a conventional computer is infeasible; however, the difficulty of these problems would not withstand the computational power of a large-scale quantum computer. To this end, the post-quantum cryptography (PQC) standardization process initiated by the National Institute of Standards and Technology (NIST) is well underway. In addition to the evaluation criteria provided by NIST, the energy consumption of these candidate algorithms is also an important criterion to consider due to the use of battery-operated devices, high-performance computing environments where energy costs are critical, as well as in the interest of green computing. In this paper, the energy consumption of PQC candidates is evaluated on an Intel Core i7-6700 CPU using PAPI, the Performance API. The energy measurements are categorized based on their proposed security level and cryptographic functionality. The results are then further subdivided based on the underlying mechanism used in order to identify the most energy-efficient schemes. Lastly, IgProf is used to identify the most energy-consuming subroutines within a select number of submissions to highlight potential areas for optimization.

An adaptor signature can be viewed as a signature concealed with a secret value and, by design, any two of the trio yield the other. In a multiparty setting, an initial adaptor signature allows each party to create additional adaptor signatures without the original secret. Adaptor signatures help address scalability and interoperability issues in blockchain. They can also bring some important advantages to cryptocurrencies, such as low on-chain cost, improved transaction fungibility, and fewer limitations of a blockchain’s scripting language. In this paper, we propose a new two-party adaptor signature scheme that relies on quantum-safe hard problems in coding theory. The proposed scheme uses a hash-and-sign code-based signature scheme introduced by Debris-Alazard et al. and a code-based hard relation defined from the well-known syndrome decoding problem. To achieve all the basic properties of adaptor signatures formalized by Aumayr et al., we introduce further modifications to the aforementioned signature scheme. We also give a security analysis of our scheme and its application to the atomic swap. After providing a set of parameters for our scheme, we show that it has the smallest pre-signature size compared to existing post-quantum adaptor signatures.