# Tag Info

I think you have some misunderstanding here. Finding collisions when knowing the trapdoor is a required feature, but leaking the trapoor when knowing collisions is an undesirable "feature" (which some constructions suffer from). A chameleon hash function (aka trapdoor commitment) allows you given the trapdoor to find pairs $(m,r)$ and $(m',r')$ with $m\neq ... 2 Because the function used for RSA encryption and decryption is commutative. This means that given secret key$sk$and public key$pk$for all messages$m\$ you have that $$D(E(m,pk),sk)=E(D(m,sk),pk)=m.$$ This means that first encrypting a message with the public key and then decrypting the so obtained ciphertext with the corresponding secret key yields the ...