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## Passphrase guards against accessing the private key

The passphrase guards against accessing the private key

The passphrase is meant to guard the private key in the event of physical accessphysical access. If the hacker has accesscan sign on to your server and can access your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

## The public key algorithm guards against deriving the private key

The public key algorithm guards against deriving the private key

If the hacker does not have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. This due to the clever way the RSA algorithm is set up. The relationship from the private key to the public key is a trap door function, meaning it is easy to compute it one direction but not in the other.

Here is an example. If I told you that X * Y = 3014569, and X and Y are integers, could you tell me X or Y? It would be very difficult (because of the way I chose X and Y). On the other hand, if I told you X = 1237 and Y = 2437, it would be very easy for you to tell me that X * Y = 3014569 (you just need to multiply!) So it's easy one way, hard the other way. This is known as the prime factorization problem.

## But he could do this

That being said, he could spend a few thousand years going through the trap door over and over to find your private key. Like this:

1. Iterate through all possible private keys
2. For each private key, derive the public key
3. Check the computed public key against the targeted public key

This is called a brute force attack. It would take a long time.

There may be some shortcuts (e.g. use a quantum computer) and mathematicians are always coming up with new ways to get around things like this. But for now, a 4096-bit key is considered plenty long to last into the foreseeable future (see this link for details).

## Passphrase guards against accessing the private key

The passphrase is meant to guard the private key in the event of physical access. If the hacker has access to your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

## The public key algorithm guards against deriving the private key

If the hacker does not have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. This due to the clever way the RSA algorithm is set up. The relationship from the private key to the public key is a trap door function, meaning it is easy to compute it one direction but not in the other.

Here is an example. If I told you that X * Y = 3014569, and X and Y are integers, could you tell me X or Y? It would be very difficult (because of the way I chose X and Y). On the other hand, if I told you X = 1237 and Y = 2437, it would be very easy for you to tell me that X * Y = 3014569 (you just need to multiply!) So it's easy one way, hard the other way.

## But he could do this

That being said, he could spend a few thousand years going through the trap door over and over to find your private key. Like this:

1. Iterate through all possible private keys
2. For each private key, derive the public key
3. Check the computed public key against the targeted public key

This is called a brute force attack. It would take a long time.

There may be some shortcuts (e.g. use a quantum computer) and mathematicians are always coming up with new ways to get around things like this. But for now, a 4096-bit key is considered plenty long to last into the foreseeable future (see this link for details).

The passphrase guards against accessing the private key

The passphrase is meant to guard the private key in the event of physical access. If the hacker can sign on to your server and can access your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

The public key algorithm guards against deriving the private key

If the hacker does not have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. This due to the clever way the RSA algorithm is set up. The relationship from the private key to the public key is a trap door function, meaning it is easy to compute it one direction but not in the other.

Here is an example. If I told you that X * Y = 3014569, and X and Y are integers, could you tell me X or Y? It would be very difficult (because of the way I chose X and Y). On the other hand, if I told you X = 1237 and Y = 2437, it would be very easy for you to tell me that X * Y = 3014569 (you just need to multiply!) So it's easy one way, hard the other way. This is known as the prime factorization problem.

That being said, he could spend a few thousand years going through the trap door over and over to find your private key. Like this:

1. Iterate through all possible private keys
2. For each private key, derive the public key
3. Check the computed public key against the targeted public key

This is called a brute force attack. It would take a long time.

There may be some shortcuts (e.g. use a quantum computer) and mathematicians are always coming up with new ways to get around things like this. But for now, a 4096-bit key is considered plenty long to last into the foreseeable future (see this link for details).

3 added 361 characters in body

## Passphrase guards against accessing the private key

The passphrase is meant to guard the private key in the event of physical access. If the hacker has access to your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

## The public key algorithm guards against deriving the private key

If the hacker does not have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. This due to the clever way the RSA algorithm is set up. The relationship from the private key to the public key is a trap door function, meaning it is easy to compute it one direction but not in the other.

Here is an example. If I told you that X * Y = 3014569, and X and Y are integers, could you tell me X or Y? It would be very difficult (because of the way I chose X and Y). On the other hand, if I told you X = 1237 and Y = 2437, it would be very easy for you to tell me that X * Y = 3014569. (you just need to multiply!) So it's easy one way, hard the other way.

## But he could do this

That being said, he could spend a few thousand years iteratinggoing through all possible private keys, deriving the public key for each,trap door over and will eventually come upon yoursover to find your private key. But that Like this:

1. Iterate through all possible private keys
2. For each private key, derive the public key
3. Check the computed public key against the targeted public key

This is called a brute force attack. It would take a LOOONNGGGlong time. A

There may be some shortcuts (e.g. use a quantum computer) and mathematicians are always coming up with new ways to get around things like this. But for now, a 4096-bit key is considered plenty long to last into the foreseeable future (see this link for details). Unless they have a quantum computer, which are not yet generally available.

## Passphrase guards against accessing the private key

The passphrase is meant to guard the private key in the event of physical access. If the hacker has access to your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

## The public key algorithm guards against deriving the private key

If the hacker does not have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. This due to the clever way the RSA algorithm is set up. The relationship from the private key to the public key is a trap door function, meaning it is easy to compute it one direction but not in the other.

Here is an example. If I told you that X * Y = 3014569, could you tell me X or Y? It would be very difficult (because of the way I chose X and Y). On the other hand, if I told you X = 1237 and Y = 2437, it would be very easy for you to tell me that X * Y = 3014569. So it's easy one way, hard the other way.

## But he could do this

That being said, he could spend a few thousand years iterating through all possible private keys, deriving the public key for each, and will eventually come upon yours. But that would take a LOOONNGGG time. A 4096-bit key is plenty long to last into the foreseeable future (see this link for details). Unless they have a quantum computer, which are not yet generally available.

## Passphrase guards against accessing the private key

The passphrase is meant to guard the private key in the event of physical access. If the hacker has access to your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

## The public key algorithm guards against deriving the private key

If the hacker does not have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. This due to the clever way the RSA algorithm is set up. The relationship from the private key to the public key is a trap door function, meaning it is easy to compute it one direction but not in the other.

Here is an example. If I told you that X * Y = 3014569, and X and Y are integers, could you tell me X or Y? It would be very difficult (because of the way I chose X and Y). On the other hand, if I told you X = 1237 and Y = 2437, it would be very easy for you to tell me that X * Y = 3014569 (you just need to multiply!) So it's easy one way, hard the other way.

## But he could do this

That being said, he could spend a few thousand years going through the trap door over and over to find your private key. Like this:

1. Iterate through all possible private keys
2. For each private key, derive the public key
3. Check the computed public key against the targeted public key

This is called a brute force attack. It would take a long time.

There may be some shortcuts (e.g. use a quantum computer) and mathematicians are always coming up with new ways to get around things like this. But for now, a 4096-bit key is considered plenty long to last into the foreseeable future (see this link for details).

2 added 361 characters in body

## Passphrase guards against accessing the private key

The passphrase is meant to guard the private key in the event of physical access. If If the hacker has access to your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

## The public key algorithm guards against deriving the private key

If the hacker does notnot have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. HeThis due to the clever way the RSA algorithm is set up. The relationship from the private key to the public key is a trap door function, meaning it is easy to compute it one direction but not in the other.

Here is an example. If I told you that X * Y = 3014569, could howeveryou tell me X or Y? It would be very difficult (because of the way I chose X and Y). On the other hand, if I told you X = 1237 and Y = 2437, it would be very easy for you to tell me that X * Y = 3014569. So it's easy one way, hard the other way.

## But he could do this

That being said, he could spend a few thousand years iterating through all possible private keys, deriving the public key for each, and will eventually come upon yours. But that would take a LOOONNGGG time. A 4096-bit key is plenty long to last into the foreseeable future (see this link for details). Unless they have a quantum computer, which are not yet generally available.

The passphrase is meant to guard the private key in the event of physical access. If the hacker has access to your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

If the hacker does not have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. He could however spend a few thousand years iterating through all possible private keys, deriving the public key for each, and will eventually come upon yours. But that would take a LOOONNGGG time. A 4096-bit key is plenty long to last into the foreseeable future (see this link for details). Unless they have a quantum computer, which are not yet generally available.

## Passphrase guards against accessing the private key

The passphrase is meant to guard the private key in the event of physical access. If the hacker has access to your certificate store, he could use the passphrase to obtain a copy of the certificate that would include the private key. Hopefully hackers don't routinely have access to your certificate store, but sometimes a hacker is just a disgruntled employee.

## The public key algorithm guards against deriving the private key

If the hacker does not have access to your certificate store, and only has the passphrase and the public key, it is not possible to derive the private key. This due to the clever way the RSA algorithm is set up. The relationship from the private key to the public key is a trap door function, meaning it is easy to compute it one direction but not in the other.

Here is an example. If I told you that X * Y = 3014569, could you tell me X or Y? It would be very difficult (because of the way I chose X and Y). On the other hand, if I told you X = 1237 and Y = 2437, it would be very easy for you to tell me that X * Y = 3014569. So it's easy one way, hard the other way.

## But he could do this

That being said, he could spend a few thousand years iterating through all possible private keys, deriving the public key for each, and will eventually come upon yours. But that would take a LOOONNGGG time. A 4096-bit key is plenty long to last into the foreseeable future (see this link for details). Unless they have a quantum computer, which are not yet generally available.

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