5 ms·

Come on! Not only your math is ridiculous (you can't just square amounts of money, just consider how it would work if you changed currency: $8 is 1260¥, squares

Come on! Not only your math is ridiculous (you can't just square amounts of money, just consider how it would work if you changed currency: $8 is 1260¥, squares it makes it 1587000¥ which is $10k != $64) but believing that RSA-2048 is factorizable in $4k is hilarious. > none of it is "brute force" It's not exhaustive search like it would be for symmetric encryption, but it's still somewhat brute-force (especially since RSA keys are inflated in size compared to symmetric encryption to accommodate for their vulnerabilities), put more clearly what I meant was “not without theoretical breakthrough unknown to the public”. BTW, it's not a very good idea to lecture people with actual crypto knowledge (even though mine is quite rusty now for I have not done any serious stuff for 15 years) when your own comes from ill-understood YouTube vulgarization videos.

DarkmSparks 2y ago
I personally factored 512 bit numbers in 2007 for a lot less than $8, so tbh I'm going to say your overestimation of your knowledge of cryptology is far more hilarious than my paranoia about the potential truth of claims made by people claiming to be experts in cryoptology. Your claim that factoring a 256bit number would cost fractions of a cent rather than my claim of roughly $3 is also very easily verifiable. Further I'll note you sound exactly like the kind of person insisting diffie hillman was a good key exchange mechanism prior to Snowdens disclosures. good luck with that.
- littlestymaar 2y ago
  I'm charitably sharing this to you: https://news.ycombinator.com/item?id=42645216 https://news.ycombinator.com/item?id=42645216 because someone actually interested in learning things asked the right question. May you sleep less ignorant tonight. > Further I'll note you sound exactly like the kind of person insisting diffie hillman was a good key exchange mechanism prior to Snowdens disclosures. good luck with that. Before or after Snowden, Diffie-Hellman (it's Martin Hellman with an “e”) is a good key exchange mechanism! When using it on Z/pZ as field it's not the most practical one nowadays because you need big keys to get the desired security level (exactly the same problem as RSA), but you if you use an elliptic curves instead you can use shorter keys again (and this is exactly what ECDH is doing: it litterally means Elliptic Curve Diffie Hellman! Diffie-Hellman went nowhere).
  - DarkmSparks 2y ago
    ->Before or after Snowden, Diffie-Hellman (it's Martin Hellman with an “e”) is a good key exchange mechanism! Meanwhile, ~10 years ago https://weakdh.org/imperfect-forward-secrecy-ccs15.pdf https://weakdh.org/imperfect-forward-secrecy-ccs15.pdf After a week-long precomputation for a specified 512-bit group, we can compute arbitrary discrete logs in that group in about a minute. We find that 82% of vulnerable servers use a single 512-bit group, allowing us to compromise connections to 7% of Alexa Top Million HTTPS sites. In response, major browsers are being changed to reject short groups. We go on to consider Diffie-Hellman with 768- and 1024-bit groups. We estimate that even in the 1024-bit case, the computations are plausible given nation-state resources.
    - littlestymaar 2y ago
      512 was known to be too low for a looong time, why do you think it was the export-grade security? 1024 being at risk against state-level adversaries isn't shocking to anyone, but there's a significant gap between this and costing $64, and this gap is much bigger than 10 years of Moore's Law (NSA had much more than 32*$64 of available compute ;). You're making grandiose claims and there's nothing that holds in your reasoning, it really feels like I'm discussing physics with a flat-earther…
bmacho 2y ago
> (you can't just square amounts of money, just consider how it would work if you changed currency: $8 is 1260¥, squares it makes it 1587000¥ which is $10k != $64) What can you square then? For example, can you square lengths? E.g. 1km is 1000m, what is its square?
- littlestymaar 2y ago
  1km² aka 1,000,000m², note how the resulting units aren't km and m but square kilometers and square meters. > What can you square then? In that case it's the number of operations (which is unitless) that must be squared and then multiplied by the cost of each operation. For instance (figures are completely made up for illustration purpose) if one individual operation costs 0.1 cent, and you have 8000 ops for the factorization, it costs $8, and the operation number squared means you have 64,000,000 operations, and the total cost is $64k. In practice we're talking about trillions of very cheap operations but when you square that number you get an insanely big number which even multiplied by a small individual cost ends up costing trillions of dollars, putting it out of reach of factorization from anyone.
  - DarkmSparks 2y ago
    the search space is p1×p2 = cost therefore (p1^2) x (p2^2) = (p1xp2)^2 =cost^2 and gnfs search cost increases in cost by (roughly) the square of the number of bits.
    - littlestymaar 2y ago
      I'll keep trying to explain it to you: you cannot take the square of a price. If my Yuan exchange rate example didn't convince you, let's have a few thoughts experiments: - let say you can do can do some amount of work for less than $1 (maybe even factoring a 512 bits number) let's call that amount of work X, and you do it for say $0.9. Do you think you can do X² work for price^2, which is $0.81 ? Yes, much more work for less than the price of doing X, isn't that magical? - a hard drive with 1TB of storage costs $40. Do you think you can have 1 Yottabyte (10^12 squared is 10^24) of storage for just $1600? There's a reason to all these paradoxes, it simply makes no sense to take the square of a sum of money, because you can't pay it in square dollars.

DarkmSparks 2y ago

I personally factored 512 bit numbers in 2007 for a lot less than $8, so tbh I'm going to say your overestimation of your knowledge of cryptology is far more hilarious than my paranoia about the potential truth of claims made by people claiming to be experts in cryoptology. Your claim that factoring a 256bit number would cost fractions of a cent rather than my claim of roughly $3 is also very easily verifiable. Further I'll note you sound exactly like the kind of person insisting diffie hillman was a good key exchange mechanism prior to Snowdens disclosures. good luck with that.

littlestymaar 2y ago
I'm charitably sharing this to you: https://news.ycombinator.com/item?id=42645216 https://news.ycombinator.com/item?id=42645216 because someone actually interested in learning things asked the right question. May you sleep less ignorant tonight. > Further I'll note you sound exactly like the kind of person insisting diffie hillman was a good key exchange mechanism prior to Snowdens disclosures. good luck with that. Before or after Snowden, Diffie-Hellman (it's Martin Hellman with an “e”) is a good key exchange mechanism! When using it on Z/pZ as field it's not the most practical one nowadays because you need big keys to get the desired security level (exactly the same problem as RSA), but you if you use an elliptic curves instead you can use shorter keys again (and this is exactly what ECDH is doing: it litterally means Elliptic Curve Diffie Hellman! Diffie-Hellman went nowhere).
- DarkmSparks 2y ago
  ->Before or after Snowden, Diffie-Hellman (it's Martin Hellman with an “e”) is a good key exchange mechanism! Meanwhile, ~10 years ago https://weakdh.org/imperfect-forward-secrecy-ccs15.pdf https://weakdh.org/imperfect-forward-secrecy-ccs15.pdf After a week-long precomputation for a specified 512-bit group, we can compute arbitrary discrete logs in that group in about a minute. We find that 82% of vulnerable servers use a single 512-bit group, allowing us to compromise connections to 7% of Alexa Top Million HTTPS sites. In response, major browsers are being changed to reject short groups. We go on to consider Diffie-Hellman with 768- and 1024-bit groups. We estimate that even in the 1024-bit case, the computations are plausible given nation-state resources.
  - littlestymaar 2y ago
    512 was known to be too low for a looong time, why do you think it was the export-grade security? 1024 being at risk against state-level adversaries isn't shocking to anyone, but there's a significant gap between this and costing $64, and this gap is much bigger than 10 years of Moore's Law (NSA had much more than 32*$64 of available compute ;). You're making grandiose claims and there's nothing that holds in your reasoning, it really feels like I'm discussing physics with a flat-earther…

bmacho 2y ago

> (you can't just square amounts of money, just consider how it would work if you changed currency: $8 is 1260¥, squares it makes it 1587000¥ which is $10k != $64) What can you square then? For example, can you square lengths? E.g. 1km is 1000m, what is its square?

littlestymaar 2y ago
1km² aka 1,000,000m², note how the resulting units aren't km and m but square kilometers and square meters. > What can you square then? In that case it's the number of operations (which is unitless) that must be squared and then multiplied by the cost of each operation. For instance (figures are completely made up for illustration purpose) if one individual operation costs 0.1 cent, and you have 8000 ops for the factorization, it costs $8, and the operation number squared means you have 64,000,000 operations, and the total cost is $64k. In practice we're talking about trillions of very cheap operations but when you square that number you get an insanely big number which even multiplied by a small individual cost ends up costing trillions of dollars, putting it out of reach of factorization from anyone.
- DarkmSparks 2y ago
  the search space is p1×p2 = cost therefore (p1^2) x (p2^2) = (p1xp2)^2 =cost^2 and gnfs search cost increases in cost by (roughly) the square of the number of bits.
  - littlestymaar 2y ago
    I'll keep trying to explain it to you: you cannot take the square of a price. If my Yuan exchange rate example didn't convince you, let's have a few thoughts experiments: - let say you can do can do some amount of work for less than $1 (maybe even factoring a 512 bits number) let's call that amount of work X, and you do it for say $0.9. Do you think you can do X² work for price^2, which is $0.81 ? Yes, much more work for less than the price of doing X, isn't that magical? - a hard drive with 1TB of storage costs $40. Do you think you can have 1 Yottabyte (10^12 squared is 10^24) of storage for just $1600? There's a reason to all these paradoxes, it simply makes no sense to take the square of a sum of money, because you can't pay it in square dollars.