either well studied isogeny problems that are believed to be hard or based on novel well motivated

to explore the construction and security of these cryptographic systems and has gained attraction

based on isogenies between elliptic curves. The fundamental idea is that the problem of finding

to prove their security. These constrained problems are tasked to find an isogeny that has some

SQISign parameters only attain 128 bits of classical security. With our techniques, we are able

Nearly all of public-key cryptosystems that are being used for real-world applications are not

based on isogenies or could do with an improvement. This not only includes novel constructions

additional structure. We note that some of these constrained problems have proved detrimental

updatable public-key encryption scheme. We prove the security of these constructions based on

believed to be resistant to quantum adversaries. The field of post-quantum cryptography aims