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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 ...


3

This is a very abstract and wrong analogy and I assume you are talking about encryption. Often for introducing public key encryption one encounters the "box with lock" example: You publish a box and a lock (your public key) and everyone can put something in the box and close the lock and send it to you. You (the only guy that has the key to the lock - the ...


3

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 ...


2

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 ...


1

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 ...


1

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: ( ...


1

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 ...


1

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 ...


1

I haven't heard of much work on this, but really choose any two that are based on assumptions that are independent of each other. Two candidates come to mind: ECC and lattice-based methods. These are based on assumptions that have nothing known in common (dlog vs. LWE). Additionally, one of the reasons many people are interested in lattice-based methods is ...


1

As far as I know, in a typical RSA encoding process first you transform the whole char string that is the file into a number, to be encrypted, so my assumption is that is not possible in a typical RSA encoding-decoding process. That's not typical. A typical real world RSA encryption process uses hybrid encryption, encrypting the data with a single-use ...



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