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Update: My previous answer, although technically true, didn't answer your question. The issue is that the strong-DDH is not hard when using pairing groups, so my answer was merely stating that your problem is at least as hard as an easy problem (duh!) After some thought, I realized your problem is at least as hard as the 2-weak Bilinear Diffie-Hellman ...


TL;DR, you don't. At this point, we have algorithms we believe are unbroken by current adversaries. For hashing, this includes the SHA-2 family of hashes, SHA-3, BLAKE2b and others. For authentication, we have the HMAC family of functions, the UMAC family of functions, Poly1305, and others. For symmetric encryption, we have AES, ChaCha20, and others. For ...

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