13 questions linked to/from Chinese Remainder Theorem and RSA
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### What information is needed to be stored for RSA private key for decryption

I am using rsa module in Python. I use the following line to generate public and private key: ...
131 views

### Faster alternatives to RSA trapdoor permutation

We're working on web3.0 decentralized internet, a big part of which is a decentralized file storage system where clients upload files to storage providers and pay them for the services. Storage ...
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### Creating hash data signatures using RSA-CRT

I have taken two prime numbers p=137 q=131 M=64 and i want to create a digital signature ...
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### Could someone please elaborate on how $(c^d \bmod n) \bmod p = c^d \bmod p$, given that $n = pq$, where $p$ and $q$ are prime numbers?

I'm following this (Chinese Remainder Theorem and RSA) post, but I don't understand how $(c^d \bmod n) \bmod p = c^d \bmod p$. Being told that it's because $n=pq$ is not enough for me to understand. ...
217 views

### Montgomery Multiplication with CRT

I am attempting to understand how to use Montgomery multiplication in an RSA private key operation: $X \equiv a^{e} \pmod{n}$ where $a$ is the message, $e$ is the exponent, $n$ is the modulus. Using ...
801 views

### What is the private key in RSA?

I'm new to cryptography and I have a doubt: I read some pages a bit different definition for the RSA private key: In 1 - (n, d) In 2 - ...
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### Space needed to store an RSA private key

How much space is actually needed to store a $4096$-bit RSA private key? I originally assumed $0.512$ kB since $\frac{4096}{8} = 512$, but then I started to wonder whether it was in hex. Simply, what'...
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### Why do we need Euler's totient function $\varphi(N)$ in RSA?

After we calculated $N = p * q$, we calculate $\varphi(N)$ and use it later to determine $e$ (PR) and $d$ (PU). But why? For decryption and encryption, we only use $N$ and don't need $\varphi(N)$. So ...
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### Is encryption time greater than decryption time?

Is encryption time always greater than decryption time for all encryption techniques (AES / DES / RSA / DSA), or is there a mistake somewhere in my implementation?