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### On a diffie hellman related oracle

Well, if the Oracle works with an arbitrary base 'g', then it is easy. If we give the Oracle the base $g^x$, and ask it to 'invert' $g$ with respect to that base, that is: The base is $h = g^x$ The ...
• 148k
1 vote

### Is shared secret and SKEYID are same in the IPSec?

First off, you are asking about IKEv1, which is an obsolete protocol - everything should be using IKEv2 instead (which does things quite differently). However, as to how IKEv1 generates SKEYID (which ...
• 148k

### How do I solve a discrete log using pen paper for exam without bruteforcing it?

Use brute force plus common sense. It is likely that the question has been specially chosen for this. With this modulus, multiplying an even number by 10 halves it. Multiplying an odd number by 10 ...

### Why does Diffie-Hellman need be a cyclic group?

Carefully selected (more in next para) cyclic groups $\{g^0,g^1,g^a,..., g^b, ...\}$ are used because in these groups finding the discrete logarithm of a group element is computationally hard, i.e. ...
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### How do I solve a discrete log using pen paper for exam without bruteforcing it?

You could try Baby-Step Giant-Step: First calculate $10^b$ for $b=0\dots 4$: $1, 10, 10\cdot 10 = 5, 10\cdot 5 = 12, 10\cdot 12 = 6$, and store them in a table manner ($\alpha_i = 10^i \bmod 19$). ...
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### Why does it take longer to generate suitably large primes for Diffie-Hellman key exchange as opposed to for RSA encryption / decryption?

generating arbitrarily large primes for DH typically takes much longer than for RSA Yes. That's for several reasons For comparable security, the prime $p$ in DH needs to have about as many bits as ...
• 142k
Accepted

### Why does it take longer to generate suitably large primes for Diffie-Hellman key exchange as opposed to for RSA encryption / decryption?

The question specifically states that generating arbitrarily large primes for DH typically takes much longer than for RSA, and I am to verify this claim. Well, yes. In the simplest terms, to ...
• 148k
1 vote

### Why does it take longer to generate suitably large primes for Diffie-Hellman key exchange as opposed to for RSA encryption / decryption?

The complexity of generating a prime depends only on the size (bitlength) of the prime. So whether for DH or not this won't change and will be polynomial complexity (polynomial in $\log p$ see details ...
• 22.6k

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