Related Concepts
Definition
RSA public-key encryption (due to Rivest, Shamir, and Adleman) is an asymmetric encryption scheme based on the RSA trapdoor one-way permutation, and thus related to integer factoring.
Theory
One-Way Permutations
A one-way function is a function f that anyone can compute efficiently, however inverting f is hard. Such a primitive is the basis of modern cryptography, and relies on the open problem \(\mathcal{P}\) vs. \(\mathcal{N}\mathcal{P}\) (computational complexity). As a consequence, any \(\mathcal{N}\mathcal{P}\)-complete problem should lead to such a one-way function candidate. Unfortunately, \(\mathcal{N}\mathcal{P}\)-complete problems are not so convenient for cryptographic applications, because either they are hard to solve for very large instances only, or very few instances are hard but the problem is easy on average. Furthermore, such a primitive is not enough for public-key encryption.
A trapdoor one-waypermutation...
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Recommended Reading
Bellare M, Rogaway P (1995) Optimal asymmetric encryption–how to encrypt with RSA. In: De Santi A (ed) Advances in cryptology–EUROCRYPT’94. Lecture notes in computer science, vol 950. Springer, Berlin, pp 92–111
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Rivest R, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public key cryptosystems. Commun ACM 21(2):120–126
Wiener M (1990) Cryptanalysis of short RSA secret exponents. IEEE Trans Inform Theory 36(3):553–558
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Pointcheval, D. (2011). RSA Public-Key Encryption. 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_153
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