How can I ensure order of encrypted data
i.e., Enc(m1) < Enc(m2) where m1 < m2, and all messages are integer values.
I have gone through Order Preserving Encryption discussed in Enabling Search over Encrypted Multimedia Databases.
According to the literature, for sorted data values (i.e., words), lower limit (l_w) and upper limit (U_w) are defined according to the frequency count of a word and estimated value (encoded value) is selected by Linear Spline Interpolation within the defined limits.
I am finding it hard to define lower and upper limits for the following data values. I want to encode the frequency with the range of [0 – 10,000] and DocCount with in [0 - 500]. However, I have only one data point (i.e., w_i) within each range (i.e., l_w_i to U_w_i), how can I find interpolant of the values.
DocCount Word Frequency 10 1 8 2 6 3 5 4 3 5 2 6 1 7 0 8 0 9 0 10
Is there any other way through which I can ensure order of the encrypted data. On StackOverFlow I was referred to homomorphic encryption – I am familiar with Pascal Paillier crypto system, any idea how can utilize it to preserve order among encrypted values.