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This procedure, also called signing a message, does not encrypt the message itself, thus does not ensure it cannot be read by others. Instead, a hash sum of the message is encrypted using the private key. For verifying, the recipient again calculates the hash sum of the message, and decrypts the hash sum calculated by the sender using the sender's public ...


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The stated problem is discussed in this paper, called the Scrambler-Permutation Problem.


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In practice, one can use openssl to extract the information: $ cat pubkey.txt -----BEGIN PUBLIC KEY----- MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCqGKukO1De7zhZj6+H0qtjTkVxwTCpvKe4eCZ0 FPqri0cb2JZfXJ/DgYSF6vUpwmJG8wVQZKjeGcjDOL5UlsuusFncCzWBQ7RKNUSesmQRMSGkVb1/ 3j+skZ6UtW+5u09lHNsj6tQ51s1SPrCBkedbNf0Tp0GbMJDyR4e9T04ZZwIDAQAB -----END PUBLIC KEY----- $ openssl ...


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RSA key formats are defined in at least RFC 3447 and RFC 5280. The format is based on ASN.1 and includes more than just the raw modulus and exponent. If you decode the base 64 encoded ASN.1, you will find some wrapping (like an object identifier) as well as an internal ASN.1 bitstring, which decodes as: ( ...


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The only reason you are seeing this is because you are dealing with such small primes. With primes like we would use in practice (1024 bits), the probability of this happening is very, very small. And, it can only happen when $e>\sqrt{\lambda(n)}$. Since we typically use $e=65537$ in practice, it is guaranteed to not happen. Anyways, there is no mistake ...


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If the application completely trusts the public key (e.g., runs code signed by it), then you could add "master key change" messages that can be signed by it, that make the application change it's hard-coded key. For additional security, you could require that the new key be additionally signed by a key hopefully separated from the now-compromised one - here ...


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With symmetric encryption, any key exchange protocol you run inside the encrypted channel must also be secure when run in plain text, if you want perfect forward secrecy. That means you can only rely on the previously established keys for authentication (you are using authenticated encryption, right?), but not for hiding the new keys. Diffie–Hellman key ...


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This is how it works.. For every user, there is 1 Private key and 1 Public key. The Private key is used to decrypt messages from other users. The Public key is used by everyone else to encrypt messages for that user. These keys are mathematically linked. If you have 5 users, there are 5 Private keys and 5 Public keys. Each user would have a copy of ...


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Asymmetric keys come in pairs. The public key of a pair can be used to encrypt data so that only the holder of the private key can decrypt it. If you had one private key, you'd also have exactly one public key that corresponds to it, so your answer of one public key and $n-1$ private keys per person cannot be entirely correct. The question is somewhat ...



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