There have been partial homomorphic encryption schemes for quite a while, where a limited number of operations can be performed on encrypted data, for example only addition or only multiplication.
addition of two ciphertexts
multiplication of a ciphertext by a plaintext number
When two ciphertexts are multiplied, the result decrypts to the sum of their plaintexts:
When a ciphertext is raised to the power of a plaintext, the result decrypts to the product of the two plaintexts:
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