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24

Is this number specified anywhere? It was formally specified in this RFC as the 1536 bit MODP group (although its use predates that RFC). However, from what I've seen, the 2048 bit MODP group from that same document is actually more popular. Why was this particular number picked? Well, it's a safe prime; in addition, the leading 64 bits and the ...


5

You are absolutely right! The random self-reducibility goes in the other direction, and this variant of the DDH assumption does not follow from it. I have no idea what the author was thinking when he wrote it :-). In any case, the paper has now been updated in ePrint and fixed. Thank you for catching this. I include the proof of this variant here: Consider ...


4

There are several obvious ways to optimize the search. The easiest approach would be to take advantage of the identity $g^e \cdot g = g^{e+1}$. That is, if we have already computed $g^e$, and verified that it is not the value we're looking for, then to step to $g^{e+1}$, we don't compute $g^{e+1}$ from scratch; instead, we take the $g^e$ value we have, and ...


2

The fact is that the discrete logarithm problem (DLP) is solved using different algorithms in the cases of multiplicative groups (where normal DH applies) and elliptic curves (where ECDH applies). The behavior of these algorithms is quite different. For multiplicative groups, where the NFS for logarithm is used, a huge part of the computation depends only ...


2

Approximately how large should p be? Current calculations say it's probablly possible to crack a 1024 bit prime today with NSA-level resources and there is speculation that the NSA has cracked some widely used 1024 bit primes. 2048 bit seems to be a common default these days. How often should p be changed, if ever? Every n handshakes, every m ...


1

ECDH is included in the ciphersuites, so the only answer is: yes, this should be possible. For your further research, it might help to know that Crypto.SE features a lot of Q&As related to “OpenSSL ECDH”. Also see the related documentation at the OpenSSL wiki for practical code examples showing how to use ECDH in OpenSSL, how to use the low-level APIs ...


1

This particular prime has been widely used in implementations of the Internet Key Exchange Protocol (IKE) and commonly referred to as Group 5. Group 5 has been in many devices for over a decade. Depending on your viewpoint this fact is either good or bad. It's good if you are implementing IKE and want to interoperate with other implementations of IKE. It ...


1

So, I does anybody know how to design a module for remainder operation in >verilog that computes the remainder in a single clock cycle? Any links to >literature discussing the algorithm would suffice. A nieve implementation would be something like. parameter bitwidth; input [bitwidth-1:0] a; input [bitwidth-1:0] b; output reg [bitwidth-1:0] result; reg ...



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