Key generation times vs CPU load Does the key generation time affect the CPU load in a mobile phone, an embedded device? I am searching on Google for info, but I am not fully sure that I have concluded to something.
Any generation will consume CPU, but it is rather unlikely that you will find that it slows down a modern smart phone.
Of the known algorithms - barring post-quantum cryptography - common two-prime RSA has the most CPU intense generation technique as it needs to find two large primes. However, RSA key pairs are normally used as long term, static key pairs. So generally applications only create them once in a while. And barring client authentication, they aren't required for setting up e.g. TLS connections.
Symmetric key pair generation is limited to random number generation. As long as the secure RNG doesn't block it is extremely unlikely that you'd notice any slowdowns for normal use cases with just a few keys. And if it does block it won't affect the CPU; it will only affect the application that requires the keys. (EC)DH key pair generation is relatively fast as well.
Finally, it is always possible to botch an implementation. You could try and create a random number generator that uses a lot of CPU or memory access to retrieve enough entropy. This could e.g. be used by programmers that use an API that lacks access to the normal cryptographic operations, e.g. when using a cross compatible, high level runtime.