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I am not a cryptography expert but I am interested in the field. Having said that: I am lately having an hard time understanding the actual strength of a crypto

I am not a cryptography expert but I am interested in the field. Having said that: I am lately having an hard time understanding the actual strength of a crypto suite based on the underlying problem, the sized of the material and the computation strength needed to break it either via optimization and parallelism capabilities. > The Web PKI deprecated 1024-bit RSA over a decade ago, and while I don’t know of anyone factoring a key of that size, it’s within the realm of possibility for a government or other organization with a large number of computers. Is it? How do I verify such claim? --- > Just a few days ago, someone factored the 862-bit RSA-260 key from the RSA factoring challenge. Yeah, but how much time it required? and what about the resources? It is just a number, it is not all the 861 bits n numbers.

upofadown 10d ago
This article from 2000 is about estimating what would be required to factor 1024 bit RSA: A Cost-Based Security Analysis of Symmetric and Asymmetric Key Lengths https://cr.yp.to/bib/2000/silverman.pdf https://cr.yp.to/bib/2000/silverman.pdf It was a response to the idea that 1024 bit RSA was under threat at the time.
rbtms 10d ago
As you probably know, the computing time in the worst case scenario for brute forcing a cryptographic key generally doubles by each bit added. That is, it would take twice the effort to brute-force 129 bits compared 128 bits. The security of RSA however depends on the factoring of very large numbers, and that means that for example, RSA-2048 doesn't translate into 2048 bits of security but 112 (roughly symmetric equivalent) bits based on the best factoring algorithms (for comparison, the RSA-512 the article mentions has an 56 bit equivalent and RSA-1024 has a 80 bit equivalent security, so RSA-1024 would take roughly 2^(80-56) ~= 17 million times to compute the worst-case scenario and RSA-2048 would take 2^(112-80) = 4.3 thousand million times more). According to the Wikipedia article on RSA numbers, RSA-220 (66b) was factored in 2016, RSA-230 (69b) in 2018, RSA-240 (72b) in 2019 and RSA-260 (76b) this year, which is too close to RSA-1024 (80b) to be comfortable. For RSA-250, the team reported it took "roughly 2,700 core-years, using Intel Xeon Gold 6130 CPUs at 2.1 GHz.". I am not going to (or feel qualified to) make estimates of how that would translate to RSA-1024, but it does sound plausible given enough resources.
- rurban 9d ago
  RSA-1024 about 2000 GPU years. With clusters of size 100k typical right now. https://x.com/sweis/status/2095570657367278051 https://x.com/sweis/status/2095570657367278051 Consider it broken already for AI or NSA guys
bityard 10d ago
> I am not a cryptography expert > How do I verify such claim? Step 1: Become a cryptography expert. ;)

upofadown 10d ago

This article from 2000 is about estimating what would be required to factor 1024 bit RSA: A Cost-Based Security Analysis of Symmetric and Asymmetric Key Lengths https://cr.yp.to/bib/2000/silverman.pdf https://cr.yp.to/bib/2000/silverman.pdf It was a response to the idea that 1024 bit RSA was under threat at the time.

rbtms 10d ago

As you probably know, the computing time in the worst case scenario for brute forcing a cryptographic key generally doubles by each bit added. That is, it would take twice the effort to brute-force 129 bits compared 128 bits. The security of RSA however depends on the factoring of very large numbers, and that means that for example, RSA-2048 doesn't translate into 2048 bits of security but 112 (roughly symmetric equivalent) bits based on the best factoring algorithms (for comparison, the RSA-512 the article mentions has an 56 bit equivalent and RSA-1024 has a 80 bit equivalent security, so RSA-1024 would take roughly 2^(80-56) ~= 17 million times to compute the worst-case scenario and RSA-2048 would take 2^(112-80) = 4.3 thousand million times more). According to the Wikipedia article on RSA numbers, RSA-220 (66b) was factored in 2016, RSA-230 (69b) in 2018, RSA-240 (72b) in 2019 and RSA-260 (76b) this year, which is too close to RSA-1024 (80b) to be comfortable. For RSA-250, the team reported it took "roughly 2,700 core-years, using Intel Xeon Gold 6130 CPUs at 2.1 GHz.". I am not going to (or feel qualified to) make estimates of how that would translate to RSA-1024, but it does sound plausible given enough resources.

rurban 9d ago
RSA-1024 about 2000 GPU years. With clusters of size 100k typical right now. https://x.com/sweis/status/2095570657367278051 https://x.com/sweis/status/2095570657367278051 Consider it broken already for AI or NSA guys

bityard 10d ago

> I am not a cryptography expert > How do I verify such claim? Step 1: Become a cryptography expert. ;)