Diffie-Hellman Group 25, and 26?












3














By looking at SonicWall Knowledge Base article Key exchange (DH) Groups Supported - Site to Site VPN:



It appears that our firewall supports DH group 25, and 26. Almost everywhere I've seen, they've recommended DH group 20-24 (We don't have DH group 24)



Should we use this? I don't understand how the DH group could be higher, with the same elliptical curve, but be a 224-bit algorithm vs our current 521-bit algorithm for DH group 21.










share|improve this question















migrated from security.stackexchange.com 1 hour ago


This question came from our site for information security professionals.















  • My understanding is that the only thing that really matters is the size of the prime (n-bit group). I would normally cite NIST or NSA standards, but with the US government shutdown, none of their websites are available. My intuition is that 224-bits and up are considered secure today, so you might as well go with the 224-bit group as it will have slightly better performance than the larger groups.
    – Mike Ounsworth
    4 hours ago










  • Do you control the other end of the site-to-site VPN you're trying to set up? If so, why don't you use a very complex pre-shared key? e.g.: M@Sup1rS*cr#tFu33yW(llP$@@w0rd!! or better yet, use a cryptographically secure key generator that's long...
    – thepip3r
    3 hours ago










  • Thanks @MikeOunsworth for that, though when you go to DH group 21, it's 521 bit. DH group 25 is 192 bit, and DH group 26 is 224 bit. So a lower DH group might actually be better? DH group 21 is also "only" a 512 bit algortithm vs DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is still better than 14, because it uses elliptical curve. It just then seems odd that DH group 25, and 26 use a smaller algortithm, but still use the same methodology ie: ellitpical curve.
    – wahmedBW
    3 hours ago










  • @thepip3r We do have a complex PSK, and it is wholly owned by us, however a) we'd like to be as secure as we can b) We'd need to do this for our third parties anyway.
    – wahmedBW
    3 hours ago










  • There are more questions in that comment than I can reply to, so I'll post a full answer.
    – Mike Ounsworth
    2 hours ago
















3














By looking at SonicWall Knowledge Base article Key exchange (DH) Groups Supported - Site to Site VPN:



It appears that our firewall supports DH group 25, and 26. Almost everywhere I've seen, they've recommended DH group 20-24 (We don't have DH group 24)



Should we use this? I don't understand how the DH group could be higher, with the same elliptical curve, but be a 224-bit algorithm vs our current 521-bit algorithm for DH group 21.










share|improve this question















migrated from security.stackexchange.com 1 hour ago


This question came from our site for information security professionals.















  • My understanding is that the only thing that really matters is the size of the prime (n-bit group). I would normally cite NIST or NSA standards, but with the US government shutdown, none of their websites are available. My intuition is that 224-bits and up are considered secure today, so you might as well go with the 224-bit group as it will have slightly better performance than the larger groups.
    – Mike Ounsworth
    4 hours ago










  • Do you control the other end of the site-to-site VPN you're trying to set up? If so, why don't you use a very complex pre-shared key? e.g.: M@Sup1rS*cr#tFu33yW(llP$@@w0rd!! or better yet, use a cryptographically secure key generator that's long...
    – thepip3r
    3 hours ago










  • Thanks @MikeOunsworth for that, though when you go to DH group 21, it's 521 bit. DH group 25 is 192 bit, and DH group 26 is 224 bit. So a lower DH group might actually be better? DH group 21 is also "only" a 512 bit algortithm vs DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is still better than 14, because it uses elliptical curve. It just then seems odd that DH group 25, and 26 use a smaller algortithm, but still use the same methodology ie: ellitpical curve.
    – wahmedBW
    3 hours ago










  • @thepip3r We do have a complex PSK, and it is wholly owned by us, however a) we'd like to be as secure as we can b) We'd need to do this for our third parties anyway.
    – wahmedBW
    3 hours ago










  • There are more questions in that comment than I can reply to, so I'll post a full answer.
    – Mike Ounsworth
    2 hours ago














3












3








3







By looking at SonicWall Knowledge Base article Key exchange (DH) Groups Supported - Site to Site VPN:



It appears that our firewall supports DH group 25, and 26. Almost everywhere I've seen, they've recommended DH group 20-24 (We don't have DH group 24)



Should we use this? I don't understand how the DH group could be higher, with the same elliptical curve, but be a 224-bit algorithm vs our current 521-bit algorithm for DH group 21.










share|improve this question















By looking at SonicWall Knowledge Base article Key exchange (DH) Groups Supported - Site to Site VPN:



It appears that our firewall supports DH group 25, and 26. Almost everywhere I've seen, they've recommended DH group 20-24 (We don't have DH group 24)



Should we use this? I don't understand how the DH group could be higher, with the same elliptical curve, but be a 224-bit algorithm vs our current 521-bit algorithm for DH group 21.







diffie-hellman






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 59 mins ago









kelalaka

5,57922040




5,57922040










asked 5 hours ago







wahmedBW











migrated from security.stackexchange.com 1 hour ago


This question came from our site for information security professionals.






migrated from security.stackexchange.com 1 hour ago


This question came from our site for information security professionals.














  • My understanding is that the only thing that really matters is the size of the prime (n-bit group). I would normally cite NIST or NSA standards, but with the US government shutdown, none of their websites are available. My intuition is that 224-bits and up are considered secure today, so you might as well go with the 224-bit group as it will have slightly better performance than the larger groups.
    – Mike Ounsworth
    4 hours ago










  • Do you control the other end of the site-to-site VPN you're trying to set up? If so, why don't you use a very complex pre-shared key? e.g.: M@Sup1rS*cr#tFu33yW(llP$@@w0rd!! or better yet, use a cryptographically secure key generator that's long...
    – thepip3r
    3 hours ago










  • Thanks @MikeOunsworth for that, though when you go to DH group 21, it's 521 bit. DH group 25 is 192 bit, and DH group 26 is 224 bit. So a lower DH group might actually be better? DH group 21 is also "only" a 512 bit algortithm vs DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is still better than 14, because it uses elliptical curve. It just then seems odd that DH group 25, and 26 use a smaller algortithm, but still use the same methodology ie: ellitpical curve.
    – wahmedBW
    3 hours ago










  • @thepip3r We do have a complex PSK, and it is wholly owned by us, however a) we'd like to be as secure as we can b) We'd need to do this for our third parties anyway.
    – wahmedBW
    3 hours ago










  • There are more questions in that comment than I can reply to, so I'll post a full answer.
    – Mike Ounsworth
    2 hours ago


















  • My understanding is that the only thing that really matters is the size of the prime (n-bit group). I would normally cite NIST or NSA standards, but with the US government shutdown, none of their websites are available. My intuition is that 224-bits and up are considered secure today, so you might as well go with the 224-bit group as it will have slightly better performance than the larger groups.
    – Mike Ounsworth
    4 hours ago










  • Do you control the other end of the site-to-site VPN you're trying to set up? If so, why don't you use a very complex pre-shared key? e.g.: M@Sup1rS*cr#tFu33yW(llP$@@w0rd!! or better yet, use a cryptographically secure key generator that's long...
    – thepip3r
    3 hours ago










  • Thanks @MikeOunsworth for that, though when you go to DH group 21, it's 521 bit. DH group 25 is 192 bit, and DH group 26 is 224 bit. So a lower DH group might actually be better? DH group 21 is also "only" a 512 bit algortithm vs DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is still better than 14, because it uses elliptical curve. It just then seems odd that DH group 25, and 26 use a smaller algortithm, but still use the same methodology ie: ellitpical curve.
    – wahmedBW
    3 hours ago










  • @thepip3r We do have a complex PSK, and it is wholly owned by us, however a) we'd like to be as secure as we can b) We'd need to do this for our third parties anyway.
    – wahmedBW
    3 hours ago










  • There are more questions in that comment than I can reply to, so I'll post a full answer.
    – Mike Ounsworth
    2 hours ago
















My understanding is that the only thing that really matters is the size of the prime (n-bit group). I would normally cite NIST or NSA standards, but with the US government shutdown, none of their websites are available. My intuition is that 224-bits and up are considered secure today, so you might as well go with the 224-bit group as it will have slightly better performance than the larger groups.
– Mike Ounsworth
4 hours ago




My understanding is that the only thing that really matters is the size of the prime (n-bit group). I would normally cite NIST or NSA standards, but with the US government shutdown, none of their websites are available. My intuition is that 224-bits and up are considered secure today, so you might as well go with the 224-bit group as it will have slightly better performance than the larger groups.
– Mike Ounsworth
4 hours ago












Do you control the other end of the site-to-site VPN you're trying to set up? If so, why don't you use a very complex pre-shared key? e.g.: M@Sup1rS*cr#tFu33yW(llP$@@w0rd!! or better yet, use a cryptographically secure key generator that's long...
– thepip3r
3 hours ago




Do you control the other end of the site-to-site VPN you're trying to set up? If so, why don't you use a very complex pre-shared key? e.g.: M@Sup1rS*cr#tFu33yW(llP$@@w0rd!! or better yet, use a cryptographically secure key generator that's long...
– thepip3r
3 hours ago












Thanks @MikeOunsworth for that, though when you go to DH group 21, it's 521 bit. DH group 25 is 192 bit, and DH group 26 is 224 bit. So a lower DH group might actually be better? DH group 21 is also "only" a 512 bit algortithm vs DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is still better than 14, because it uses elliptical curve. It just then seems odd that DH group 25, and 26 use a smaller algortithm, but still use the same methodology ie: ellitpical curve.
– wahmedBW
3 hours ago




Thanks @MikeOunsworth for that, though when you go to DH group 21, it's 521 bit. DH group 25 is 192 bit, and DH group 26 is 224 bit. So a lower DH group might actually be better? DH group 21 is also "only" a 512 bit algortithm vs DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is still better than 14, because it uses elliptical curve. It just then seems odd that DH group 25, and 26 use a smaller algortithm, but still use the same methodology ie: ellitpical curve.
– wahmedBW
3 hours ago












@thepip3r We do have a complex PSK, and it is wholly owned by us, however a) we'd like to be as secure as we can b) We'd need to do this for our third parties anyway.
– wahmedBW
3 hours ago




@thepip3r We do have a complex PSK, and it is wholly owned by us, however a) we'd like to be as secure as we can b) We'd need to do this for our third parties anyway.
– wahmedBW
3 hours ago












There are more questions in that comment than I can reply to, so I'll post a full answer.
– Mike Ounsworth
2 hours ago




There are more questions in that comment than I can reply to, so I'll post a full answer.
– Mike Ounsworth
2 hours ago










2 Answers
2






active

oldest

votes


















3















It appears that our firewall supports DH group 25, and 26. Almost
everywhere I've seen, they've recommended DH group 20-24 (We don't
have DH group 24)



Should we use this?




NO, stick to groups 19-21 if possible!





According to the linked resource, DH group 25 is a prime-based 192-bit elliptic curve and group 26 is a prime-based 224-bit elliptic curve. These provide a security level of 96 and 112-bit respectively, that is the best known attack will require about $2^{96}$ or $2^{112}$ curve operations. I suppose these curves were standardized as enough people complained they can't computationally or by bandwidth or storage afford to use group 19 and the probably did so after 19-21 were standardized.



Now compare this to the groups 19, 20 and 21 which use 256-, 384- and 512- bit elliptic curves which respectively offer 128, 192 and 256-bit security. This is much better at a minor cost of security. If you really can't afford to use these groups for performance reasons, then the 224-bit group should be fine, as its security is comparable to 2048-bit classic DH / RSA and the 192-bit group is risky as its security could be broken by a sufficiently determined attacker with sufficient funding, usually this is attributed to nation-state attackers.




DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is
still better than 14, because it uses elliptical curve.




Group 14 uses classic finite-field diffie-hellman, i.e. $g^xbmod p$ for a 2048-bit prime $p$. Because this operation exposes so much structure, there are attacks that are more efficient than the generic ones, which is all that works against elliptic curves. These attacks are so good, that a 2048-bit prime modulus for DH has roughly a 112-bit security level, which roughly corresponds to a 224-bit elliptic curve, e.g. group 26. Also note that due to these more scalable attacks, group 1 is actually breakable, even by academics and group 2 which has a 80-bit security level due to its 1024-bit modulus has a decent chance of being breakable by a determined attack with sufficient funding. Also due to the nature of these attacks, it is sufficient if the attacker once does one big pre-computation for the parameter set and can then break individual DH instances very easily, think 1 week of pre-computation to solve each instance in 90 seconds afterwards.






share|improve this answer





















  • This is much better at a minor cost of security sounds strange, was it meant to say "at a minor cost of performance"?
    – Ella Rose
    2 mins ago



















2














I am not familiar with each of the named DH groups ("group 21", "group 25", etc) but to my knowledge none of them are broken, so this answer assumes that all groups of the same bit-strength have equivalent security.



DH vs ECDH



Traditional Diffie-Hellman (DH) is based on reversing multiplications / exponents on very large numbers (formally called the Discrete Logarithm problem). This is where you see group sizes like 2048-bit.



Elliptic Curve Diffie-Hellman (ECDH) is based on the mathematical problem of point multiplication on elliptic curves. This is where you see group sizes like 224-bit. Because of the added complexity of doing multiplications on elliptic curves rather than straight integers, ECDH can get the same security using much smaller numbers.



Here is a comparison of security levels:



Table comparing security levels of DH and ECDH



From that table, 2048-bit DH is the same security level as 224-bit ECDH, and was estimated to be ~112 bits of security whenever NIST put together that table. So according to that, you could get away with a 2048/224 bit DH/ECDH group, but 3072/256 bit would be more conservative.



Pros / Cons



For the same security level (say DH 2048 vs ECDH 224) the ECDH will get you better performance (faster, less server load, etc) simply because the numbers to multiply are smaller. So if you have the choice, go for an ECDH group, and go for the smallest one that meets your security needs -- if you are doing "normal" e-commerce type things, then a 256-bit ECDH group will be more than enough.






share|improve this answer





















  • Traditional Diffie-Hellman (DH) is based on the mathematical problem of factoring prime numbers. DH is based on the discrete logarithm problem, not factoring. Also, it's easy to factor a prime number - simply output the number and you are done
    – Ella Rose
    1 hour ago










  • Whoops, right, DH != RSA. Thanks. Also #veryFunny
    – Mike Ounsworth
    1 hour ago











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2 Answers
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active

oldest

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2 Answers
2






active

oldest

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active

oldest

votes






active

oldest

votes









3















It appears that our firewall supports DH group 25, and 26. Almost
everywhere I've seen, they've recommended DH group 20-24 (We don't
have DH group 24)



Should we use this?




NO, stick to groups 19-21 if possible!





According to the linked resource, DH group 25 is a prime-based 192-bit elliptic curve and group 26 is a prime-based 224-bit elliptic curve. These provide a security level of 96 and 112-bit respectively, that is the best known attack will require about $2^{96}$ or $2^{112}$ curve operations. I suppose these curves were standardized as enough people complained they can't computationally or by bandwidth or storage afford to use group 19 and the probably did so after 19-21 were standardized.



Now compare this to the groups 19, 20 and 21 which use 256-, 384- and 512- bit elliptic curves which respectively offer 128, 192 and 256-bit security. This is much better at a minor cost of security. If you really can't afford to use these groups for performance reasons, then the 224-bit group should be fine, as its security is comparable to 2048-bit classic DH / RSA and the 192-bit group is risky as its security could be broken by a sufficiently determined attacker with sufficient funding, usually this is attributed to nation-state attackers.




DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is
still better than 14, because it uses elliptical curve.




Group 14 uses classic finite-field diffie-hellman, i.e. $g^xbmod p$ for a 2048-bit prime $p$. Because this operation exposes so much structure, there are attacks that are more efficient than the generic ones, which is all that works against elliptic curves. These attacks are so good, that a 2048-bit prime modulus for DH has roughly a 112-bit security level, which roughly corresponds to a 224-bit elliptic curve, e.g. group 26. Also note that due to these more scalable attacks, group 1 is actually breakable, even by academics and group 2 which has a 80-bit security level due to its 1024-bit modulus has a decent chance of being breakable by a determined attack with sufficient funding. Also due to the nature of these attacks, it is sufficient if the attacker once does one big pre-computation for the parameter set and can then break individual DH instances very easily, think 1 week of pre-computation to solve each instance in 90 seconds afterwards.






share|improve this answer





















  • This is much better at a minor cost of security sounds strange, was it meant to say "at a minor cost of performance"?
    – Ella Rose
    2 mins ago
















3















It appears that our firewall supports DH group 25, and 26. Almost
everywhere I've seen, they've recommended DH group 20-24 (We don't
have DH group 24)



Should we use this?




NO, stick to groups 19-21 if possible!





According to the linked resource, DH group 25 is a prime-based 192-bit elliptic curve and group 26 is a prime-based 224-bit elliptic curve. These provide a security level of 96 and 112-bit respectively, that is the best known attack will require about $2^{96}$ or $2^{112}$ curve operations. I suppose these curves were standardized as enough people complained they can't computationally or by bandwidth or storage afford to use group 19 and the probably did so after 19-21 were standardized.



Now compare this to the groups 19, 20 and 21 which use 256-, 384- and 512- bit elliptic curves which respectively offer 128, 192 and 256-bit security. This is much better at a minor cost of security. If you really can't afford to use these groups for performance reasons, then the 224-bit group should be fine, as its security is comparable to 2048-bit classic DH / RSA and the 192-bit group is risky as its security could be broken by a sufficiently determined attacker with sufficient funding, usually this is attributed to nation-state attackers.




DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is
still better than 14, because it uses elliptical curve.




Group 14 uses classic finite-field diffie-hellman, i.e. $g^xbmod p$ for a 2048-bit prime $p$. Because this operation exposes so much structure, there are attacks that are more efficient than the generic ones, which is all that works against elliptic curves. These attacks are so good, that a 2048-bit prime modulus for DH has roughly a 112-bit security level, which roughly corresponds to a 224-bit elliptic curve, e.g. group 26. Also note that due to these more scalable attacks, group 1 is actually breakable, even by academics and group 2 which has a 80-bit security level due to its 1024-bit modulus has a decent chance of being breakable by a determined attack with sufficient funding. Also due to the nature of these attacks, it is sufficient if the attacker once does one big pre-computation for the parameter set and can then break individual DH instances very easily, think 1 week of pre-computation to solve each instance in 90 seconds afterwards.






share|improve this answer





















  • This is much better at a minor cost of security sounds strange, was it meant to say "at a minor cost of performance"?
    – Ella Rose
    2 mins ago














3












3








3







It appears that our firewall supports DH group 25, and 26. Almost
everywhere I've seen, they've recommended DH group 20-24 (We don't
have DH group 24)



Should we use this?




NO, stick to groups 19-21 if possible!





According to the linked resource, DH group 25 is a prime-based 192-bit elliptic curve and group 26 is a prime-based 224-bit elliptic curve. These provide a security level of 96 and 112-bit respectively, that is the best known attack will require about $2^{96}$ or $2^{112}$ curve operations. I suppose these curves were standardized as enough people complained they can't computationally or by bandwidth or storage afford to use group 19 and the probably did so after 19-21 were standardized.



Now compare this to the groups 19, 20 and 21 which use 256-, 384- and 512- bit elliptic curves which respectively offer 128, 192 and 256-bit security. This is much better at a minor cost of security. If you really can't afford to use these groups for performance reasons, then the 224-bit group should be fine, as its security is comparable to 2048-bit classic DH / RSA and the 192-bit group is risky as its security could be broken by a sufficiently determined attacker with sufficient funding, usually this is attributed to nation-state attackers.




DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is
still better than 14, because it uses elliptical curve.




Group 14 uses classic finite-field diffie-hellman, i.e. $g^xbmod p$ for a 2048-bit prime $p$. Because this operation exposes so much structure, there are attacks that are more efficient than the generic ones, which is all that works against elliptic curves. These attacks are so good, that a 2048-bit prime modulus for DH has roughly a 112-bit security level, which roughly corresponds to a 224-bit elliptic curve, e.g. group 26. Also note that due to these more scalable attacks, group 1 is actually breakable, even by academics and group 2 which has a 80-bit security level due to its 1024-bit modulus has a decent chance of being breakable by a determined attack with sufficient funding. Also due to the nature of these attacks, it is sufficient if the attacker once does one big pre-computation for the parameter set and can then break individual DH instances very easily, think 1 week of pre-computation to solve each instance in 90 seconds afterwards.






share|improve this answer













It appears that our firewall supports DH group 25, and 26. Almost
everywhere I've seen, they've recommended DH group 20-24 (We don't
have DH group 24)



Should we use this?




NO, stick to groups 19-21 if possible!





According to the linked resource, DH group 25 is a prime-based 192-bit elliptic curve and group 26 is a prime-based 224-bit elliptic curve. These provide a security level of 96 and 112-bit respectively, that is the best known attack will require about $2^{96}$ or $2^{112}$ curve operations. I suppose these curves were standardized as enough people complained they can't computationally or by bandwidth or storage afford to use group 19 and the probably did so after 19-21 were standardized.



Now compare this to the groups 19, 20 and 21 which use 256-, 384- and 512- bit elliptic curves which respectively offer 128, 192 and 256-bit security. This is much better at a minor cost of security. If you really can't afford to use these groups for performance reasons, then the 224-bit group should be fine, as its security is comparable to 2048-bit classic DH / RSA and the 192-bit group is risky as its security could be broken by a sufficiently determined attacker with sufficient funding, usually this is attributed to nation-state attackers.




DH group 14, which is a 2048 bit algortithm, however I read that DH group 21 is
still better than 14, because it uses elliptical curve.




Group 14 uses classic finite-field diffie-hellman, i.e. $g^xbmod p$ for a 2048-bit prime $p$. Because this operation exposes so much structure, there are attacks that are more efficient than the generic ones, which is all that works against elliptic curves. These attacks are so good, that a 2048-bit prime modulus for DH has roughly a 112-bit security level, which roughly corresponds to a 224-bit elliptic curve, e.g. group 26. Also note that due to these more scalable attacks, group 1 is actually breakable, even by academics and group 2 which has a 80-bit security level due to its 1024-bit modulus has a decent chance of being breakable by a determined attack with sufficient funding. Also due to the nature of these attacks, it is sufficient if the attacker once does one big pre-computation for the parameter set and can then break individual DH instances very easily, think 1 week of pre-computation to solve each instance in 90 seconds afterwards.







share|improve this answer












share|improve this answer



share|improve this answer










answered 33 mins ago









SEJPM

28.3k554132




28.3k554132












  • This is much better at a minor cost of security sounds strange, was it meant to say "at a minor cost of performance"?
    – Ella Rose
    2 mins ago


















  • This is much better at a minor cost of security sounds strange, was it meant to say "at a minor cost of performance"?
    – Ella Rose
    2 mins ago
















This is much better at a minor cost of security sounds strange, was it meant to say "at a minor cost of performance"?
– Ella Rose
2 mins ago




This is much better at a minor cost of security sounds strange, was it meant to say "at a minor cost of performance"?
– Ella Rose
2 mins ago











2














I am not familiar with each of the named DH groups ("group 21", "group 25", etc) but to my knowledge none of them are broken, so this answer assumes that all groups of the same bit-strength have equivalent security.



DH vs ECDH



Traditional Diffie-Hellman (DH) is based on reversing multiplications / exponents on very large numbers (formally called the Discrete Logarithm problem). This is where you see group sizes like 2048-bit.



Elliptic Curve Diffie-Hellman (ECDH) is based on the mathematical problem of point multiplication on elliptic curves. This is where you see group sizes like 224-bit. Because of the added complexity of doing multiplications on elliptic curves rather than straight integers, ECDH can get the same security using much smaller numbers.



Here is a comparison of security levels:



Table comparing security levels of DH and ECDH



From that table, 2048-bit DH is the same security level as 224-bit ECDH, and was estimated to be ~112 bits of security whenever NIST put together that table. So according to that, you could get away with a 2048/224 bit DH/ECDH group, but 3072/256 bit would be more conservative.



Pros / Cons



For the same security level (say DH 2048 vs ECDH 224) the ECDH will get you better performance (faster, less server load, etc) simply because the numbers to multiply are smaller. So if you have the choice, go for an ECDH group, and go for the smallest one that meets your security needs -- if you are doing "normal" e-commerce type things, then a 256-bit ECDH group will be more than enough.






share|improve this answer





















  • Traditional Diffie-Hellman (DH) is based on the mathematical problem of factoring prime numbers. DH is based on the discrete logarithm problem, not factoring. Also, it's easy to factor a prime number - simply output the number and you are done
    – Ella Rose
    1 hour ago










  • Whoops, right, DH != RSA. Thanks. Also #veryFunny
    – Mike Ounsworth
    1 hour ago
















2














I am not familiar with each of the named DH groups ("group 21", "group 25", etc) but to my knowledge none of them are broken, so this answer assumes that all groups of the same bit-strength have equivalent security.



DH vs ECDH



Traditional Diffie-Hellman (DH) is based on reversing multiplications / exponents on very large numbers (formally called the Discrete Logarithm problem). This is where you see group sizes like 2048-bit.



Elliptic Curve Diffie-Hellman (ECDH) is based on the mathematical problem of point multiplication on elliptic curves. This is where you see group sizes like 224-bit. Because of the added complexity of doing multiplications on elliptic curves rather than straight integers, ECDH can get the same security using much smaller numbers.



Here is a comparison of security levels:



Table comparing security levels of DH and ECDH



From that table, 2048-bit DH is the same security level as 224-bit ECDH, and was estimated to be ~112 bits of security whenever NIST put together that table. So according to that, you could get away with a 2048/224 bit DH/ECDH group, but 3072/256 bit would be more conservative.



Pros / Cons



For the same security level (say DH 2048 vs ECDH 224) the ECDH will get you better performance (faster, less server load, etc) simply because the numbers to multiply are smaller. So if you have the choice, go for an ECDH group, and go for the smallest one that meets your security needs -- if you are doing "normal" e-commerce type things, then a 256-bit ECDH group will be more than enough.






share|improve this answer





















  • Traditional Diffie-Hellman (DH) is based on the mathematical problem of factoring prime numbers. DH is based on the discrete logarithm problem, not factoring. Also, it's easy to factor a prime number - simply output the number and you are done
    – Ella Rose
    1 hour ago










  • Whoops, right, DH != RSA. Thanks. Also #veryFunny
    – Mike Ounsworth
    1 hour ago














2












2








2






I am not familiar with each of the named DH groups ("group 21", "group 25", etc) but to my knowledge none of them are broken, so this answer assumes that all groups of the same bit-strength have equivalent security.



DH vs ECDH



Traditional Diffie-Hellman (DH) is based on reversing multiplications / exponents on very large numbers (formally called the Discrete Logarithm problem). This is where you see group sizes like 2048-bit.



Elliptic Curve Diffie-Hellman (ECDH) is based on the mathematical problem of point multiplication on elliptic curves. This is where you see group sizes like 224-bit. Because of the added complexity of doing multiplications on elliptic curves rather than straight integers, ECDH can get the same security using much smaller numbers.



Here is a comparison of security levels:



Table comparing security levels of DH and ECDH



From that table, 2048-bit DH is the same security level as 224-bit ECDH, and was estimated to be ~112 bits of security whenever NIST put together that table. So according to that, you could get away with a 2048/224 bit DH/ECDH group, but 3072/256 bit would be more conservative.



Pros / Cons



For the same security level (say DH 2048 vs ECDH 224) the ECDH will get you better performance (faster, less server load, etc) simply because the numbers to multiply are smaller. So if you have the choice, go for an ECDH group, and go for the smallest one that meets your security needs -- if you are doing "normal" e-commerce type things, then a 256-bit ECDH group will be more than enough.






share|improve this answer












I am not familiar with each of the named DH groups ("group 21", "group 25", etc) but to my knowledge none of them are broken, so this answer assumes that all groups of the same bit-strength have equivalent security.



DH vs ECDH



Traditional Diffie-Hellman (DH) is based on reversing multiplications / exponents on very large numbers (formally called the Discrete Logarithm problem). This is where you see group sizes like 2048-bit.



Elliptic Curve Diffie-Hellman (ECDH) is based on the mathematical problem of point multiplication on elliptic curves. This is where you see group sizes like 224-bit. Because of the added complexity of doing multiplications on elliptic curves rather than straight integers, ECDH can get the same security using much smaller numbers.



Here is a comparison of security levels:



Table comparing security levels of DH and ECDH



From that table, 2048-bit DH is the same security level as 224-bit ECDH, and was estimated to be ~112 bits of security whenever NIST put together that table. So according to that, you could get away with a 2048/224 bit DH/ECDH group, but 3072/256 bit would be more conservative.



Pros / Cons



For the same security level (say DH 2048 vs ECDH 224) the ECDH will get you better performance (faster, less server load, etc) simply because the numbers to multiply are smaller. So if you have the choice, go for an ECDH group, and go for the smallest one that meets your security needs -- if you are doing "normal" e-commerce type things, then a 256-bit ECDH group will be more than enough.







share|improve this answer












share|improve this answer



share|improve this answer










answered 2 hours ago









Mike Ounsworth

2,1201923




2,1201923












  • Traditional Diffie-Hellman (DH) is based on the mathematical problem of factoring prime numbers. DH is based on the discrete logarithm problem, not factoring. Also, it's easy to factor a prime number - simply output the number and you are done
    – Ella Rose
    1 hour ago










  • Whoops, right, DH != RSA. Thanks. Also #veryFunny
    – Mike Ounsworth
    1 hour ago


















  • Traditional Diffie-Hellman (DH) is based on the mathematical problem of factoring prime numbers. DH is based on the discrete logarithm problem, not factoring. Also, it's easy to factor a prime number - simply output the number and you are done
    – Ella Rose
    1 hour ago










  • Whoops, right, DH != RSA. Thanks. Also #veryFunny
    – Mike Ounsworth
    1 hour ago
















Traditional Diffie-Hellman (DH) is based on the mathematical problem of factoring prime numbers. DH is based on the discrete logarithm problem, not factoring. Also, it's easy to factor a prime number - simply output the number and you are done
– Ella Rose
1 hour ago




Traditional Diffie-Hellman (DH) is based on the mathematical problem of factoring prime numbers. DH is based on the discrete logarithm problem, not factoring. Also, it's easy to factor a prime number - simply output the number and you are done
– Ella Rose
1 hour ago












Whoops, right, DH != RSA. Thanks. Also #veryFunny
– Mike Ounsworth
1 hour ago




Whoops, right, DH != RSA. Thanks. Also #veryFunny
– Mike Ounsworth
1 hour ago


















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