Maximum Security of RSA

crypt

2/2/24, 5:30 AM

Table 2 of NIST SP-800 56B provides Estimated Maximum Security Strength of different modulus sizes. It means that RSA-3072 provides security of 128-bits at Max.

Is it the case for symmetric algorithms also? Like AES-128 provides security strength of 128 bits at maximum? or is it like AES-128 provides security strength of 128 bits at minimum?

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aes

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Crypto

kodlu

2/2/24, 7:39 AM

Since a brute force key search for AES-128 by definition takes $2^{128}$ encryptions in the worst case since that is the number of possible keys and one of the keys must be the right now (and approximately $2^{127}$ encryptions on average) for AES this is actually a maximum.

However these one-dimensional numbers (time complexity only) ignore space (i.e., memory) complexities required. For AES-128, we can iterate through possible keys one by one, so memory required is essentially constant. The best attacks on public key cryptosystems typically require a lot of memory as well.

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crypt

2/3/24, 3:51 AM

and in both cases, its maximum security not the minimum security.

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: Maximum Security of RSA

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