Suppose Anubha and Braj decide to do key-exchange using Diffie Hellman scheme except for the choice of group used. Instead of using F^*_p as in Diffie-Hellman, they use S_n, the group of permutations of numbers in the range [1, n]. It is well-known that |Sn| = n! and therefore, even for n = 100, the group has very large size. The key-exchange happens as follows: An element g ∈ Sn is chosen such that g has large order, say l. Anubha randomly chooses a random number c ∈ [1, l − 1], and sends g^c to Braj. Braj chooses another random number d ∈ [1, l−1] and sends g^d to Anubha. Anhuba computes k = (g^d)^c and Braj computes k = (g^c)^d.

Show that an attacker Ela can compute the key k efficiently.

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