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The answer to both questions lies in understanding entropy, and how entropy is gathered to create a key. (And, of course, how well the implementation does so without bugs.) Each operating system creates and maintains a pool of entropy from which the entropy – also known as “randomness” – is tapped in the process of generating the key. Also, to the extent ...


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if someone generates the same RSA key pair as someone else, then ... someone will have the same RSA key pair as someone else. when someone generates a key pair, how can he/she be sure that nobody has already generated this key pair? The exact same ways he/she can generate any unique value. Proof: Let the unique value be the key pair, or let the ...


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Since $p$ and $q$ are primes, the only factors you needs to rule out are those two numbers. Suppose $p$ divides $(p-1)(q-1)$. Then it divides either $p-1$ (clearly not true) or $q-1$. The latter means $q-1 = p \cdot x$, for some $x \ge 2$ (if $x = 1$ either $p$ or $q$ is even, which is only possible if the numbers are 2 and 3). However, then $q \ge 2p+1$, ...


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Put another way, you can say that the key is whatever information the recipient possesses which allows him to decrypt the message, and which must be kept secret from everybody else. Thus, "algorithm" and "key" are not mutually exclusive: if knowledge of the algorithm allows one to decrypt a message, then the algorithm is the key.


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Picking up what has been said in the comments: to simplify: symmetric ciphers are like mathematical operations with 2 operands and 1 result. There is The plaintext message $m$ and $k$ as the key and they result in the ciphertext $c$. In your example, the algorithm can be cut down to a addition and modulo: $c = (m + k) \mod k_{max}$ And of course there is ...


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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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Your description of how RFC 5959 works isn't quite right. It is not quite correct to state that RFC 5959 encrypts using AES in ECB mode. A correct statement is: if the plaintext is exactly 128 bits, then use ECB mode, otherwise use a non-trivial mode of operation found in RFC 3394. In the former case, ECB mode is fine, since it's just a single block of ...



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