In 1995, Shor discovered an algorithm that would enable a sufficiently powerful quantum computer to attack all public-key cryptographic schemes based on discrete logarithm and prime factorisation, such as RSA and elliptic curves that are widely used today. Isogeny-based cryptography provides a quantum resistant alternative. In 2022, the Supersingular
Isogeny Diffie-Hellman (SIDH) key exchange proposed to the NIST competition came under major attacks. Far from hindering the future of isogeny-based cryptography, these attacks gave a major boost to research in this field. The ideas behind these highly effective attacks actually inspired new cryptographic schemes and improvements to existing ones that do not suffer from SIDH's security weaknesses. Leveraging these new techniques, our works contributed to improvements of Short Quaternion Isogeny Signatures (SQIsign), a digital signature scheme recently selected to the third round of the NIST competition. As a result, SQIsign became faster, safer and even more compact than it already was. Our works also contributed to the design and implementation of fast algorithms to compute isogenies in dimensions 2 and 4 that made SQIsign improvements effective, with broader cryptographic applications beyond SQIsign.