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I am given $p = 4916335901$, $q = 88903$ and am asked to show these are prime To check whether a given integer $n$ is prime you have to check whether it is only divisible by $1$ and $n$, i.e., that it is not a composite integer. If you are given such an integer you can either factor the given integer, use primality tests to check for primality or in ...

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Well, if the hash function is weak, then the attacker might be able to take a valid signature for a signed message, and find a second message for which the signature for this first would also validate for the second. For example, if Alice signs the message "I like chocolate", what Bob might do is find a second message "Alice owes Bob $13,106,107.57", and ... 3 According to this answer, RSA with the "usual" "padding scheme, described in PKCS#1 as the 'old-style, v1.5' padding," can be made to satisfy that; one would need to specify NULL or omission and require that the public exponent's prime factors are all easily findable and sufficiently bigger than the 4th root of the modulus. 2 It depends. If the entire input itself is within a DER encoded structure, then I would bug out. There is nothing defined for BER, CER or DER that would allow padding of structures within constructed values. If the input is just followed by additional data or junk bytes then it is up to the protocol or otherwise your discretion if you want to accept the ... 2 I don't think there's an exact "correct" behaviour in this case. It would be up to the implementation to decide, since the spec is only concerned about the DER encoded portion. If your implementation parses the input as it moves along only, and doesn't concern itself with the overall size, then it would work fine. Having said that, I believe the best ... 1 With my new idea I seem to solve the problem and answer my question, so I'll go ahead and post it as the answer. I choose the new$m'$as$m'=t+m$with$t>0$. Now the verification works like this:$v'=g^{m'w} y^{rw}=g^{m'w+xrw}=g^{tw+mw+xrw}=g^{tw} \cdot g^k=r' \mod q$So my new$r'=g^{tw}r=g^{ts^{-1}}r$This means I can create a legit signature to any ... 1 What you need to know is that all equations in this context are, implicitly, understood to be modulo n. That information alone should answer all of your questions, starting with the equation k = (z1 - z2) / (s1 - s2) (modulo N), which hence means k = ((z1-z2) * modular_inverse_mod_n(s1-s2)) % n, where I tried to copy your modulus (%) operator. Specifically: ... 1 While no SHA1 collisions have been found, there are some attacks: ~$2^{60}$collision attack. Estimated to cost around \$1-2 million currently in the cloud. Possibly economical soon, especially with specialized hardware. Intractable preimage attacks like $2^{151}$ against reduced round variant, $2^{159}$ against full hash. (Cf. $2^{160}$ brute force on any ...

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In the case of emails your solution is not really practical. The problem is that the sender of an email uses the public key whereas the receiver should have the secret key. This means that whenever somebody wants to send you an email (and therefore generate a new key) you have to be online or you have to provide a set of pre-computed key pairs. If multiple ...

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