I am new to bulletproofs. From what I understand, if I was to do a range proof using bulletproofs, both the start and end number have to be a power of 2.

is there any algorithm/approach which can be used to expand this to numbers that are not powers of 2?

Example: find if a number is in the range 18 to 65?

  • 2
    $\begingroup$ You can use an AND statement to do this. Give your number x, prove that (x-18) > 0 AND (65-x) > 0 . Bulletproofs can be used with arithmetic circuits, so you could build the statement above $\endgroup$
    – user69644
    Aug 15, 2019 at 16:33
  • $\begingroup$ yes, that's it thanks, how do i accept your answer? don't see an option $\endgroup$ Nov 19, 2019 at 9:59
  • $\begingroup$ I added it as an answer $\endgroup$
    – user69644
    Nov 19, 2019 at 13:44

1 Answer 1


You can use an AND statement to do this.

To prove that x is between a and b , you can prove that (x-a) > 0 AND (b-x) > 0


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