System and methods for entropy and statistical quality metrics in physical unclonable function generated bitstrings

Abstract

The Distribution Effect is proposed for the HELP PUF that is based on purposely introducing biases in the mean and range parameters of path delay distributions to enhance entropy. The biased distributions are then used in the bitstring construction process to introduce differences in the bit values associated with path delays that would normally remain fixed. Offsets are computed to fine tune a token's digitized path delays as a means of maximizing entropy and reproducibility in the generated bitstrings: a first population-based offset method computes median values using data from multiple tokens (i.e., the population) and a second chip-specific technique is proposed which fine tunes path delays using enrollment data from the authenticating token.

1 . A Physically Unclonable Function (PUF) method for authentication between a token by a server, the method comprising the steps of:
 storing, by the server, a set of path delays from a plurality of tokens in a secure database;   selecting, by the server, a set of path delays, wherein the selected set defines a distribution;   measuring, by the server, both a mean value and a range value of the path delay distribution;   applying, by the server, a linear transformation to the path delay distribution that subtracts the measured mean value from each path delay and divides each path delay by the measured range value to provide offset values;   adding, by the server, the offset values to the path delays to shift the path delay distribution; and   generating, by the token, a bitstring from the path delays, wherein a value of each bit of the bitstring depends on the shifted distribution.   
     
     
         2 . The PUF method of authentication according to  claim 1 , wherein the linear transformation creates a dependency between both the path delay distribution and a final form of the path delays produced by the linear transformation. 
     
     
         3 . The PUF method of authentication according to  claim 1 , wherein the path delay distribution depends on the lengths of the paths selected. 
     
     
         4 . The PUF method of authentication according to  claim 1 , wherein the shifted distributions of the path delays maximizes entropy of each bit of the generated bitstring. 
     
     
         5 . The PUF method of authentication according to  claim 1 , wherein user defined parameters are used to apply different transformation to one or more path delays. 
     
     
         6 . The PUF method of authentication according to  claim 1 , wherein the linear transformation further comprises the step of creating standardized values from the path delay distribution using the equation: 
       
         
           
             
               
                 zval 
                 i 
               
               = 
               
                 
                   ( 
                   
                     
                       PND 
                       i 
                     
                     - 
                     
                       μ 
                       chip 
                     
                   
                   ) 
                 
                 
                   Rng 
                   chip 
                 
               
             
           
         
         wherein PND i  is an original path delay distribution, μ chip  is a mean parameter, Rng chip , is a range parameter, and zval i , is a standardized value. 
       
     
     
         7 . The PUF method of authentication according to  claim 6 , wherein one or more standardized values zval i  are transformed into fixed point values using the equation
   PND c=z val i Rng ref +μ ref  
   wherein is PNDc is the original path delay distribution compensated for temperature and voltage, μ ref  is a mean parameter of PNDc, and Rng ref  is a range parameter of PNDc.