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Yes, the problem of multicast one-way authentication can be solved using symmetric cryptography only, assuming any one of the following applies: you trust each receiving party to hold a common secret key secret, and not to use it nefariously; or you accept overhead in the broadcast message growing linearly with the number $n$ of recipients, in the order of ...

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To randomly guess a single key from a 128-bit key space has a chance of 1 divided by the number of elements or $\frac{1} {2^{128}}$ where $2^{128}$ is the number of keys possible. To get ballpark figures to convert between base 2 exponents and base 10 exponents you can use the following trick: Because $2^{10} = 1024 \approx 10^3$ you can easily count the ...

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The concept of using an asymmetric key (RSA) to encrypt a symmetric key (AES) is not new. This was first popularized by PGP, which is probably what I would encourage you to use to solve your problem. SSH (well SFTP in particular) also uses a somewhat similar approach and could also be pressed into transmitting files securely. Pretty much any approach you ...

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(1) is the correct answer. The Vengiere cipher phrase is a distractor. Basically all alphabets are in the cipher. Note that the key does not need to be infinite, merely the same length as the plaintext and random. So in that regard, all of the answers are incorrect... But (1) is the "best" answer as it is the answer with the most entropy or randomness, ...

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The answer is to your problem is called Transport Layer Security with Pre-Shared Keys (TLS-PSK) and is widely available in implementations. TLS-PSK offers PKC aided and non-aided key-exchanges, with the former being recognizable by the DHE, ECDHE, RSA parts in their names. This means you want to look for the TLS_PSK_WITH_* cipher suites. In particular I'd ...

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