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Joe
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I'm going to assume this isn't possible, but I have to ask because I'm trying to fundamentally understand what I've thus far been trying to implement by following an RFC.

SRP-6a starts off with declaring that I should choose $N$, a sufficiently large prime, and $g$, a generator. Let's say $N$ is 1024-bits and $g$ is 2. A sufficiently random number $a$ is generated. For arguments sake I chose the length of $a$ to be 128 bits. My public key $A$ is then given as $g^a mod N$$g^a \bmod N$.

Now, assume that I'm the server (or in this case I'm just trying to debug an SRP-6a protocol), and I receive $A$. Since I know both $g$ and $N$, can I determine $a$ (in a reasonable amount of time). I'm guessing absolutely not, but it would be nice to know precisely why.

I'm going to assume this isn't possible, but I have to ask because I'm trying to fundamentally understand what I've thus far been trying to implement by following an RFC.

SRP-6a starts off with declaring that I should choose $N$, a sufficiently large prime, and $g$, a generator. Let's say $N$ is 1024-bits and $g$ is 2. A sufficiently random number $a$ is generated. For arguments sake I chose the length of $a$ to be 128 bits. My public key $A$ is then given as $g^a mod N$.

Now, assume that I'm the server (or in this case I'm just trying to debug an SRP-6a protocol), and I receive $A$. Since I know both $g$ and $N$, can I determine $a$ (in a reasonable amount of time). I'm guessing absolutely not, but it would be nice to know precisely why.

I'm going to assume this isn't possible, but I have to ask because I'm trying to fundamentally understand what I've thus far been trying to implement by following an RFC.

SRP-6a starts off with declaring that I should choose $N$, a sufficiently large prime, and $g$, a generator. Let's say $N$ is 1024-bits and $g$ is 2. A sufficiently random number $a$ is generated. For arguments sake I chose the length of $a$ to be 128 bits. My public key $A$ is then given as $g^a \bmod N$.

Now, assume that I'm the server (or in this case I'm just trying to debug an SRP-6a protocol), and I receive $A$. Since I know both $g$ and $N$, can I determine $a$ (in a reasonable amount of time). I'm guessing absolutely not, but it would be nice to know precisely why.

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Joe
Joe
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Discovering private exponent from public key

I'm going to assume this isn't possible, but I have to ask because I'm trying to fundamentally understand what I've thus far been trying to implement by following an RFC.

SRP-6a starts off with declaring that I should choose $N$, a sufficiently large prime, and $g$, a generator. Let's say $N$ is 1024-bits and $g$ is 2. A sufficiently random number $a$ is generated. For arguments sake I chose the length of $a$ to be 128 bits. My public key $A$ is then given as $g^a mod N$.

Now, assume that I'm the server (or in this case I'm just trying to debug an SRP-6a protocol), and I receive $A$. Since I know both $g$ and $N$, can I determine $a$ (in a reasonable amount of time). I'm guessing absolutely not, but it would be nice to know precisely why.