A Modified Threshold RSA Digital Signature Scheme

Threshold cryptography provides a way in which the secret key of an organization or a company can be shared practically. Threshold signatures are part of the threshold cryptography. Solutions for the case of the RSA scheme are especially important because of its widespread use. However, for RSA modulus n=pq , the ring Z φ(n) is not a field, an element in it may not have inverse. At the same time, since φ(n) is a secret parameter that the signature participants should not know, the participants can not do the arithmetic modulo φ(n) . These problems cause some difficulties in setting up secret sharing schemes over Z φ(n) , then in setting up threshold RSA signature schemes. This paper presents a new technique to overcome the difficulties mentioned above. At first, it introduces a safe hash function; then sets up a RSA signature scheme with a particular form. Finally, combining the above two points, a new threshold RSA signature scheme is got. Differing from the previous methods, these methods need not to invert any element in any structure (such as Z φ(n) ), and then no algebraic extensions are needed for any structures, which provides us some convenience in implementation.