I'm currently reading the work "Obfuscation of probabilistic circuits and Applications' by Canetti Lin Tessaro and Vaikuntanathan 2015. It says sub exponentially hard OWF implies sub exponentially hard PRF ( puncturable PRF) and later again proves that sub exponentially hard PRF ( puncturable PRF) implies sub exponentially hard iO.

I'm really confused with what the author means by the term "subexponentially hard" and is it a weather or a stronger assumption when it comes to the OWF or iO.

Thanks in advance

I'm currently reading the work "Obfuscation of probabilistic circuits and Applications' by Canetti Lin Tessaro and Vaikuntanathan 2015. It says sub exponentially hard OWF implies sub exponentially hard PRF ( puncturable PRF) and later again proves that sub exponentially hard PRF ( puncturable PRF) + sub exponentially hard iO $\implies$ pIO(probabilistic circuits).

I'm really confused with what the author means by the term "subexponentially hard" and is it a weather or a stronger assumption when it comes to the OWF or iO.

Thanks in advance