I am studying finalist algorithms of NIST Post-Quantum Cryptography Standardization. I noticed that almost all third party cryptanalysis papers consist of side-channel attacks. Why are classical cryptanalysis methods -algebraic, mathematical attacks etc.- more effective on classical algorithms than post-quantum algorithms?
In addition, I know that mathematical problems behind post-quantum algorithms are relatively new - at least for cryptography- but domination of side channel attacks in literature forced me to consider that "Is there any characteristical property of post-quantum algorithms that makes them more vulnerable to side-channel attacks?"
Finally, I am open to any advice for beginning side-channel resistant implementation techniques -especially for post quantum algorithms-.