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Definitions In RSA, an encryption key is a pair of integers $(N,e)$ with $N$ the product of $m\ge2$ distinct odds secret primes $r_i$ (with $0<i\le m$), and $e$ is such that $\gcd(e,\lambda(N))=1$ where $\lambda(N)=\operatorname{lcm}(r_1-1,\dots,r_m-1)$ is the Charmichael function. It follows that $e$ is odd. Typically, other conditions are added, like ...


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I think that there is no chance of getting such an asymmetric cipher simply because you forgot about science. The security on todays asymmetric cryptography is mostly based on the assumption that some mathematical algorithms cannot be reversed (e.g. the discrete logarithm or integer factorization). If mathematics solves this problems then the algorithm is ...


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If an appropriate padding mechanism is used then you cannot directly encrypt the private key with the public key as the input size would be too large. If hybrid encryption is used (RSA + AES) then the answer is no. You could possibly raise (modulo $n$) the private exponent to the power of the public exponent. So then you would need to retrieve $d$ from $d ^ ...


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A keyspace is the set of all possible keys; it's a set. The cardinality of the keyspace is an integer, and is the number of elements in the keyspace. There is no possibility of confusion, because one is a set and the other is an integer.


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The site also misrepresents RSA encryption. If you are using textbook RSA (i.e. this scheme, with no padding), you don't independently encrypt each letter. Rather, you take the entire message, treat it as a number, and encrypt that. This doesn't work if your primes are 3 and 11, but if they're each, say, 8 bytes long, then you could encrypt a 16-byte ...


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You are correct that in this case simple frequency analysis would be possible since textbook RSA encryption is deterministic. One can get around this by using RSA with random padding. Here are a few references: Why is padding used for RSA encryption given that it is not a block cipher? OAEP Why RSA encryption padding is critical In practice, we ...


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Nope, you can always restrict your message space to a subset of the message space for which the scheme is defined (which is the case here). Note that in practice you will deal with messages relatively prime to $N$, i.e., from $\mathbb{Z}_N^*$, anyways (any message not coprime to $N$ - except zero - would allow you to factor $N$ - thus its very unlikely to ...


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If we signed a secret message $m$ by publishing its signature $σ$ computed as $m^d\bmod N$, at least two very bad things would happen: The message would not be so secret anymore That's because anyone knows the public key $(N,e)$, and thus from $σ$ can compute $σ^e\bmod N$, which is $m\bmod N$. This reveals a lot of information about $m$, which goes ...


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openssl rsa -pubin -inform PEM -text -noout < public_key.pem Public-Key: (64 bit) Modulus: 16513720463601767803 (0xe52c8544a915157b) Exponent: 65537 (0x10001) The modulus is small enough that you can easily factor it After finding the prime factors, you can calculate the private exponent After you have the private exponent, you raise each 64-bit block ...


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... are secure for up to 30 years. Unfortunately, you didn't reference where this number comes from. Breaking asymmetric cryptosystems comes with various flavors: Scientific advances and new records, e.g. the factorization of RSA-768 in 2009 What intelligence agencies are capable of (it can be assumed to be a few years ahead of scientific advances, ...


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Great question. I'll answer it in several parts. Which Keys does Alice send? There are two cryptographic operations that Alice may want to do: encryption/decryption, and signing/validation. You can either use the same keypair for both, or have two separate pairs of keys. 1 keypair method: Here Alice would sign outgoing messages, and decrypt incoming ...


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Alice sends a CSR (certificate signing request) to the CA, which contains her public key, her name and usually her location. This CSR is then signed to prove ownership of the associated private key. The CA uses the data in the CSR to derive a certificate which will be handed to the user afterwards. The user can then prove his identity. The CA needs to ...


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At first, the abbreviation “ABBE” is used by Zhou et al. in [2] as a name for his ABE scheme. Zhou builds on top of a CP-ABE scheme which in addition supports “constant” ciphertexts (named CCP-ABE). From this perspective ABBE is a specific ABE scheme based on CP-ABE supporting constant ciphertexts. However, in a more general way, I see ABE in the context of ...


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Of course, it is possible. It is possible to take a public key encryption algorithm which takes the private key and the known ciphertext into the known plaintext, convert that into a set of equations in $GF(2)$ with the private key as unknown variables, and solve for those unknown variables. Alternatively, you can take the key generation algorithm, which ...



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