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  1. Free, publicly-accessible full text available December 2, 2025
  2. Recent attacks have shown that SIKE is not secure and should not be used in its current state. However, this work was completed before these attacks were discovered and might be beneficial to other cryptosystems such as SQISign. The primary downside of SIKE is its performance. However, this work achieves new SIKE speed records even using less resources than the state-of-the-art. Our approach entails designing and optimizing a new field multiplier, SIKE-optimized Keccak unit, and high-level controller. On a Xilinx Virtex-7 FPGA, this architecture performs the NIST Level 1 SIKE scheme key encapsulation and key decapsulation functions in 2.23 and 2.39 ms, respectively. The combined key encapsulation and decapsulation time is 4.62 ms, which outperforms the next best Virtex-7 implementation by nearly 2 ms. Our implementation achieves speed records for the NIST Level 1, 2, and 3 parameter sets. Only our NIST Level 5 parameter set was beat by an all-out performance implementation. Our implementations also efficiently utilize the FPGA resources, achieving new records in area-time product metrics for all parameter sets. Overall, this work continues to push the bar for accelerating SIKE computations to make a stronger case for SIKE standardization.

     
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    Free, publicly-accessible full text available March 31, 2025
  3. We present new results and speedups for the large-degree isogeny computations within the extended supersingular isogeny Diffie-Hellman (eSIDH) key agreement framework. As proposed by Cervantes-Vázquez, Ochoa-Jiménez, and Rodríguez-Henríquez, eSIDH is an extension to SIDH and fourth round NIST post-quantum cryptographic standardization candidate SIKE. By utilizing multiprime large-degree isogenies, eSIDH and eSIKE are faster than the standard SIDH/SIKE and amenable to parallelization techniques that can noticeably increase their speed with multiple cores. Here, we investigate the use of multiprime isogeny strategies to speed up eSIDH and eSIKE in serial implementations. These strategies have been investigated for other isogeny schemes such as CSIDH. We apply them to the eSIDH/eSIKE scenario to speed up the multiprime strategy by about 10%. When applied to eSIDH, we achieve a 7–8% speedup for Bob’s shared key agreement operation. When applied to eSIKE, we achieve a 3–4% speedup for key decapsulation. Historically, SIDH and SIKE have been considerably slower than its competitors in the NIST PQC standardization process. These results continue to highlight the various speedups achievable with the eSIKE framework to alleviate these speed concerns. Though eSIDH and eSIKE are susceptible to the recent devastating attacks on SIKE, our analysis applies to smooth degree isogeny computations in general, and isogeny-based signature schemes which use isogenies of smooth (not necessarily powersmooth) degree. 
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  6. Problems relating to the computation of isogenies between elliptic curves defined over finite fields have been studied for a long time. Isogenies on supersingular elliptic curves are a candidate for quantum-safe key exchange protocols because the best known classical and quantum algorithms for solving well-formed instances of the isogeny problem are exponential. We propose an implementation of supersingular isogeny Diffie-Hellman (SIDH) key exchange for complete Edwards curves. Our work is motivated by the use of Edwards curves to speed up many cryptographic protocols and improve security. Our work does not actually provide a faster implementation of SIDH, but the use of complete Edwards curves and their complete addition formulae provides security benefits against side-channel attacks. We provide run time complexity analysis and operation counts for the proposed key exchange based on Edwards curves along with comparisons to the Montgomery form. 
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