Anna Rikova wrote:

maybe this is a silly question, but at the moment I don't know how to solve it. Assume there are 4 partys A,B,C,D. Now the parties B,C,D want to create a random value r for A, so that each party B,C,D can verify afterwards, that A uses indeed the random value r, but doesn't know the value of r.

I thought of the following solution, but it has a problem: Each party I \in{B,C,D} broadcasts a value g^{r_i} mod p, where r_i is random, p is a large prime and g is a generator. After that each party sends to A the value r_i secretly. Aftern that A can compute: r= r_B + r_C + r_D. If A then uses this value in the form of g^r everyone can verify that A uses every r_i in g^r.

What does it mean "A uses this value in the form of g^r"? A uses r not g^r, doesn't it? This is a weak point: from A's use of r every party should be able to compute g^r mod p with no knowledge of r. I assume you know how to organize that.

This scheme has one problem (at least I think so): The partys B,C wait till D braodcasts her value g^{r_D}. Then they choose their values r_B and r_C so that g^r has a special characteristic e.g. the last bit of g^r is zero. Then r is not randomly disributed in Z_p, cause only values are allowed for r, which yield to g^r with last bit zero.

What's about the following modification? Each party i\in{B,C,D} sends to A the value of r_i secretly. Upon receiving all three values A broadcasts q_1=g^{r_B} mod p, q_2=g^{r_C} mod p, q_3=g^{r_D} mod p. The party i then verifies that the value r_i was used to produce one of q_1, q_2, q_3. From A's use of r every party computes g^r mod p and verifies that g^r=q1*q2*q3. Max --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to [EMAIL PROTECTED]