Efficient Proofs that a Committed Number Lies in an Interval.

**Abstract:**

Alice wants to prove that she is young enough to borrow money from her bank, without revealing her age. She therefore needs a tool for proving that a committed number lies in a specific interval. Up to now, such tools were either inefficient (too many bits to compute and to transmit) or inexact (i.e. proved membership to a much larger interval). This paper presents a new proof, which is both efficient and exact. Here, "efficient" means that there are less than 20 exponentiations to perform and less than 2 kbytes to transmit. The potential areas of application of this proof are numerous (electronic cash, group signatures, publicly verifiable secret encryption, etc...).