Cryptographic method for securely comparing two integer secret data x and y, held by a first computing device and by a second computing device , respectively, said method comprising: - a step (E10) of the first computing device generating an RSA modulus, denoted N; - a step (E40) of the first computing device computing a number C equal to g b ax h 1 , where g is an element of a subgroup G of Z N of order b d , h 1 is an element of a subgroup H of Z N of order f , and a, b, d and f denote integers such that b and f are mutually prime, and the data x and y are less than d / a; - a step (E50, E50') of the first computing device sending the number C to the second computing device; - a step (F20, F20') of the second computing device computing at least: o a number D equal to C u.b d-ay ( gh 3) v h 2 , where u and v denote two random integers, and h2 and h 3 are elements of the subgroup H; and o a first fingerprint (E1) of ( gh 3) v computed using a hash function; - a step (F30, F30') of the second computing device sending the number D and the first fingerprint to the first computing device; - a step (E70, E80, E70', E80') of the first computing device computing the number ( D f ) f' , where f' is the inverse of f modulo b d ; - a step (E90, E90', E95') of the first computing device obtaining, based on the computed number ( D f ) f' , a second fingerprint (E2) using the hash function; and - a step (E100, E100') of the first computing device determining that x is greater than or equal to y or that x is less than y depending on the result of a comparison between the first fingerprint and the second fingerprint. - a step (E10) of the first computing device generating an RSA modulus, denoted N; - a step (E40) of the first computing device computing a number C equal to g b ax h 1 , where g is an element of a subgroup G of Z N of order b d , h 1 is an element of a subgroup H of Z N of order f , and a, b, d and f denote integers such that b and f are mutually prime, and the data x and y are less than d / a; - a step (E50, E50') of the first computing device sending the number C to the second computing device; - a step (F20, F20') of the second computing device computing at least: o a number D equal to C u.b d-ay ( gh 3) v h 2 , where u and v denote two random integers, and h2 and h 3 are elements of the subgroup H; and o a first fingerprint (E1) of ( gh 3) v computed using a hash function; o a number D equal to C u.b d-ay ( gh 3) v h 2 , where u and v denote two random integers, and h2 and h 3 are elements of the subgroup H; and o a first fingerprint (E1) of ( gh 3) v computed using a hash function; - a step (F30, F30') of the second computing device sending the number D and the first fingerprint to the first computing device; - a step (E70, E80, E70', E80') of the first computing device computing the number ( D f ) f' , where f' is the inverse of f modulo b d ; - a step (E90, E90', E95') of the first computing device obtaining, based on the computed number ( D f ) f' , a second fingerprint (E2) using the hash function; and - a step (E100, E100') of the first computing device determining that x is greater than or equal to y or that x is less than y depending on the result of a comparison between the first fingerprint and the second fingerprint. <EOS>