A trapdoor permutation represents a specific type of one-way function that is simple to compute in one direction but computationally difficult to reverse without a piece of secret information, termed the trapdoor. With possession of this trapdoor, reversing the function becomes computationally straightforward. These functions are fundamental to public-key cryptography, enabling secure communication and verifiable digital signatures. The inherent difficulty of inversion without the trapdoor ensures the security of encrypted data.
Context
Trapdoor permutations constitute a cornerstone of modern public-key infrastructure, underpinning algorithms such as RSA. Their security depends on complex mathematical problems that are challenging to solve without the specific trapdoor information. Ongoing discussions often revolve around the computational hardness of these underlying problems and the potential threat from quantum computing algorithms to their long-term security.
A new cryptographic primitive, permutable pseudorandom permutations, enables the first standard-model one-shot signatures, securing single-use digital transactions.
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