PUF-protected pseudo-homomorphic methods to generate session keys

A method of generating and using a cryptographic key element n at a server device having a first array of addressable PUF (physical-unclonable-function) devices, comprising:

• receiving a first message digest, the first message digest comprising information that has been iteratively subjected to a one-way cryptographic function a first predetermined number of times;
• generating, from the first message digest, a series of PUF challenges;
• applying the PUF challenges to the first array of addressable PUF devices;
• receiving a first response bitstream from the first array of addressable PUF devices corresponding to the PUF challenges;
• storing the first response bitstream;
• receiving a second message digest, the second message digest comprising the information that has been iteratively subjected to the one-way cryptographic function a second predetermined number of times, the second predetermined number of times being less than the first predetermined number of times;
• iteratively subjecting the second message digest to the one-way cryptographic function until a match is achieved to the first message digest, and identifying the key element n as the number of times the second message digest was subjected to before the match is achieved to the first message digest.