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Definition
A trapdoor one-way function is a one-way function with an additional requirement. Informally, a one-way function might be described as a function for which evaluation in one direction is straightforward, while computation in the reverse direction is far more difficult. Such a function becomes a trapdoor one-way function when one adds the requirement that computation in the reverse direction becomes straightforward when some additional (trapdoor) information is revealed.
Background
Paralleling the theoretical development of one-way functions, trapdoor one-way functions were introduced by Diffie and Hellman [1] and their implications for the development of public-key cryptography explored in that remarkable paper. The full power of trapdoor one-way functions was elegantly captured in the proposal for public-key cryptography and the introduction of digital signature schemes.
Theory
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Diffie W, Hellman ME (1976) New directions in cryptography. IEEE T Info Theory IT-22(6):644–654
Menezes AJ, van Oorschot PC, Vanstone SA (1997) Handbook of applied cryptography. CRC Press, Boca Raton
Merkle RC, Hellman ME (1978) Hiding information and signatures in trap door knapsacks. IEEE T Info Theory 24:525–530
Rivest RL, Shamir A, Adleman LM (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21:120–126
Yao AC (1982) Theory and applications of trapdoor functions. In: Proceedings of the IEEE 23rd annual symposium on foundations of computer science, Chicago, pp 80–91
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© 2011 Springer Science+Business Media, LLC
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Robshaw, M.J.B. (2011). Trapdoor One-Way Function. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_482
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DOI: https://doi.org/10.1007/978-1-4419-5906-5_482
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