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There are encryption schemes which allow you to choose the key to produce any arbitrary decryption from a given ciphertext. For a trivial example, consider the
by saulrh 9y ago
There are encryption schemes which allow you to choose the key to produce any arbitrary decryption from a given ciphertext. For a trivial example, consider the one-time pad scheme that's simply "plaintext XOR key" and "ciphertext XOR key"; by choosing a key that's equal to "plaintext XOR ciphertext" you can construct a key for any ciphertext from a plaintext or any plaintext from a ciphertext. Mr. Xi uses this to produce the just-released lottery numbers from the ciphertext regardless of the numbers or the ciphertext.
- modalduality 9y agoyup! they should have used a commitment scheme instead - for example, SHA256(winning numbers || 512-bit nonce). To reveal, reveal the winning numbers and the nonce and Mr X can check that the hash matches. The nonce is to introduce more entropy so Mr X can't just bruteforce the hash, but since finding any collision is difficult, it doesn't let the alien cheat by trying different nonces (unlike with different keys with encryption schemes).