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There is no minimal message size. Even an empty message can be securely encrypted, i.e. the ciphertext is indistinguishable from a different encrypted message, as long as the encryption key remains secret. Can you describe exactly what are want to achieve? Where will the secret key come from? Even though minor optimizations are possible with very short ...


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Whenever you see the letters ECB, you should run away screaming. This is a telltale sign that something has gone terribly, horribly wrong. The code fragment you quoted implements what we sometimes call ‘textbook RSA’, which is a polite way to discreetly announce to the cocktail partygoers that you are desperately in need of a professional cryptographer. ...


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Increasing the prime numbers does not necessarily lead to an increase in security of the RSA. As an example, when the private exponent is less than $\frac{N^{\frac{1}{4}}}{3}$, Wiener's attack is able to factor $N$ in the polynomial time. There are other attacks against this system, which can be found in "Twenty Years of Attacks on the RSA Cryptosystem" and ...


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The idea that RSA relies on the difficulty of integer factorization is called the RSA problem. The efficiency of the different methods to perform integer factorization is discussed in a similar article on Wikipedia. Theoretically, there may be more efficient methods to perform factorization; we cannot prove that there aren't. Therefore we cannot prove RSA ...


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In RSA with modulus $n$, the legitimate user's cost to encrypt a message is $(\log_2 n) (\log_2 \log_2 n)^{1 + o(1)}$ bit operations, with the best public exponent $e = 3$; and to decrypt a message (if you know the secret exponent) is $(\log_2 n) (\log_2 \log_2 n)^{2 + o(1)}$ bit operations. This is most assuredly not exponential in $n$ or even in the size $...


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The OP asks two questions. The first question is: After we calculated $N = p * q$, we calculate $\varphi(N)$ and use it later to determine $e$ (PR) and $d$ (PU). But why? This is exactly the prescription on page 6 of the original RSA paper, where $n=p\cdot q$ is the product of two (very large) prime numbers, and, hence the number of integers relatively ...


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