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Consider the following variant of DSA in which the message space is [Z q ]: To generate a signature: Choose a random number [k Zq]

Consider the following variant of DSA in which the message space is [Zq]:

To generate a signature:

  1. Choose a random number [k Zq]
  2. Calculate [r = gk mod p]
  3. Compute [s = (m + xr )k1 mod q]

The signature is [r, s] .

To verify the signature:

  1. Compute [u1 = ms1 mod q]
  2. Compute [u2 = rs1 mod q]
  3. Test whether [r = gu1 hu2 mod p]

This is not secure because the adversary, after intercepting a message [m1] and its signature [r, s], can create a valid signature [r', s'] of another message [m2]. Which of the following is correct regarding the forged signature?

1: [r' r, s' s]

2: [r' = r, s' s]

3: [r' = r , s' s]

4: [r' r, s' = s]

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