Linked Questions

1
vote
1answer
4k views

How many bits of symmetric security does RSA-3072 actually provide? [duplicate]

I know that the sizes are standardized to $1024$, $2048$ etc. but they actually provide different security than $128$, $256$... for example $\texttt{RSA-}2048$ is actually $112$ bits of security and $...
3
votes
2answers
866 views

Why are recomended RSA key lengths so high? [duplicate]

I was checking for authoritative sources to back up my recommendation of a minimum RSA key length of 1024 and was shocked to find that NIST 800-56Br1 and FIPS 186-4 both recommend at least 2048 bits ...
0
votes
1answer
594 views

Equivalent RSA modulus for NIST P-192 and P-521 elliptic curves [duplicate]

At www.keylength.com, I found the following table of ECC field size and the corresponding RSA modulus recommended by NIST. ECC Modulus RSA Prime Size 160 1024 224 2048 ...
0
votes
0answers
35 views

To get 128-bit security for RSA, the modulus should be 4096 bits. How was that determined? [duplicate]

My understanding of security level is that for a crypto scheme to have n-bit security means it would take $2^n$ operations to break it. For something like AES with a 128-bit key, it's straight-...
110
votes
7answers
65k views

How big an RSA key is considered secure today?

I think 1024 bit RSA keys were considered secure ~5 years ago, but I assume that's not true anymore. Can 2048 or 4096 keys still be relied upon, or have we gained too much computing power in the ...
25
votes
2answers
6k views

Why is it not possible to increase the size of RSA keys indefinitely?

According to this primer on elliptic curves by Ars Technica, when composite numbers get "too" big, they become easier to factorize with Quadratic Sieve and General Number Field Sieve. While this is ...
10
votes
3answers
2k views

1 Billion Bit Encryption?

So, browsing through YouTube, I stumbled on this video interview of John Draper (Captain Crunch), one of the first "hackers". He talks for about 3 minutes (until 27:48) about his home rolled ...
10
votes
1answer
21k views

How much stronger is RSA-2048 compared to RSA-1024?

How much stronger is RSA-2048 compared to RSA-1024? It is hard to imagine very big numbers. So what would be your way to explain the difference to someone who doesn't know much about cryptography?
15
votes
2answers
3k views

How do I get the equivalent strength of an ECC key?

I know how to calculate the comparable symmetric strength of an RSA modulus: calculate the running time for a field sieve. This is how NIST gives approximate symmetric sizes for asymmetric algos in ...
10
votes
1answer
5k views

How long does it take to crack RSA 1024 with a PC?

Using an Intel Core i5 CPU, how long does it take to crack RSA using a key size of 1024 bit (generated using a secure key pair generation function)? Suppose for instance that we have thousands of ...
9
votes
2answers
3k views

Why is the complexity of RSA-1024 80 bit and not 86 bit?

Why is the complexity of RSA-1024 80 bit and not 86.76611925028119 bit? Here is the complexity for the GNFS (pulled from the linked Wikipedia article): $$\exp\left( \left(\sqrt[3]{\frac{64}{...
8
votes
3answers
3k views

What does “export grade” cryptography mean? And how is this related to the Logjam attack?

I am doing some research on the Logjam attack, and I need help in learning some terms that are new for me. What does "export grade" cryptography mean? And how is this related to the Logjam attack?
5
votes
2answers
2k views

Difficulty of breaking RSA for a given key size

Is it true that breaking a 1024-bit RSA key is as difficult as breaking a 128 bit symmetric key (e.g. AES)? I know that breaking a RSA key is equivalent to factoring the modulus $N$. To factor it, you ...
5
votes
1answer
4k views

Recommended password complexity for SSH key encryption using AES-256-CBC

When protecting SSH private keys with password-based encryption, what would be a good minimum password complexity+length standard to make cracking the password too difficult to be worthwhile anytime ...
4
votes
1answer
4k views

ECC vs RSA: how to compare key sizes?

I know and I have understood the details of RSA, elliptic curve cryptography, (EC)DH and (EC)DSA. I keep reading everywhere that (if we don't consider non-deterministic computers) "ECC can achieve ...

15 30 50 per page