The motivation for finding large twin smooth integers lies in their application to compact isogeny-based post-quantum protocols. The recent key exchange scheme B-SIDH and the recent digital signature scheme SQISign both require large primes that lie between two smooth integers; finding such a prime can be seen as a special case of finding twin smooth integers under the additional stipulation that their sum is a prime $p$.
When searching for cryptographic parameters with $2^{240} \leq p <2^{256}$, an implementation of our sieve found primes $p$ where $p+1$ and $p-1$ are $2^{15}$-smooth; the smoothest prior parameters had a similar sized prime for which $p-1$ and $p+1$ were $2^{19}$-smooth.
Category / Keywords: public-key cryptography / Post-quantum cryptography, isogeny-based cryptography, Prouhet-Tarry-Escott problem, twin smooth integers, B-SIDH, SQISign Date: received 14 Oct 2020 Contact author: michael meyer at hs-rm de Available format(s): PDF | BibTeX Citation Version: 20201014:182723 (All versions of this report) Short URL: ia.cr/2020/1283