Aring oscillator based puf technology has 16 ring oscillators " the cryptographic protocol use 128-bit streams of pairs. 1) an intra-puf error rate of 7% (average error when the same pair is subject to repetitive queries to generate responses) what is the threshold t1 (maximum acceptable number of bad crp errors) needed to get frr< 1ppm? (use poisson) 2) with modified protocol the intra puf error rate is 1% what is the threshold t2 needed to get frr< 1ppm?