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5

Under the assumption that $(K,\text{Msg})\to H_K(\text{Msg})$ is a secure MAC (be it HMAC or any other MAC), and $\text{Nonce}$ does not repeat and is of fixed size, both $H_K(\text{Msg}||\text{Nonce})$ and $H_K(\text{Nonce}||\text{Msg})$ are demonstrably secure, in the sense that an adversary not knowing $K$ can't distinguish either from random, even for ...

4

Adi Shamir's secret database of all primes is to cryptography venues what the Dahu is to French summer camps. For why, see the answers to this related question. The three other future work items in the quoted presentation are in the same vein (Breaking RSA-1024 with Fermat factoring; Breaking RSA-1024 using $1024 = 2*2*2*2*2*2*2*2*2*2$; Breaking RSA-1024 ...

2

Yes, it's possible. Encrypting each line independently, like you suggest is the way to go. Most likely you will want to use a symmetric encryption algorithm independently for each line – i.e. have a new unique IV/nonce per line. That's the simplest to implement. However, it means every line is up to 128 bits longer. If you can't live with that, you ...

1

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 $q \ge 2p+1$, ...

1

You may be better off encrypting the file using normal file encryption, and then encrypting the diff that goes with the file, except for the line numbers included in the diff. You could also extract the line number changes from the diff in advance. Otherwise you will have to keep track of the lines, and make sure that the nonces used for each line stay ...

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