# Tag Info

9

It seems we have aligned interests. I'm also a university student (although I am a math/comp sci double major) looking to pursue a career in cryptography. To that end, I have been self-studying it for a while now. So, take what I say with a grain of salt. As a forewarning, this post focuses specifically on what topics cryptographers often encounter and less ...

9

In Shannon's landmark paper Communication Theory of Secrecy Systems, published in 1949, he discussed two traits of secure ciphers: confusion and diffusion. Loosely speaking, confusion means that the relationship between the symmetric key and ciphertext should be complex. Diffusion, on the other hand, focuses on the relationship between the plaintext and ...

8

A bit rotation of a $w$-bit word by $r$ bits to the right transforms a $w$-bit word $X=(x_{w-1},x_{w-2},\dots,x_1,x_0)$ into the $w$-bit word $\operatorname{ROTR}(X,r)=(x_{r+w-1\bmod w},x_{r+w-2\bmod w},\dots,x_{r+1\bmod w},x_{r\bmod w})$. Depending on context, $r$ is arbitrary in $\mathbb Z$, or constrained to some interval thereof, e.g. $0\le r<w$. ...

6

Those appear to be based on the complexity of the General Number Field Sieve, one of the fastest (if not the fastest) classical factoring algorithms. I confirmed this in Mathematica. Here is the complexity for the GNFS (pulled from the linked Wikipedia article): \exp\left( \left(\sqrt[3]{\frac{64}{9}} + o(1)\right)(\ln n)^{\frac{1}{3}}(\ln \ln ...

6

Your question is only slightly ill-defined. The problem is that the word "cryptography" is horribly overloaded. I think there are at least three different regimes of cryptography: Cryptography in academia. As Reid said, academic cryptography mainly springs out of complexity theory. With very few exceptions, you don't need much math knowledge to succeed ...

6

The quoted recommendations do little to prevent fields that are subject to the recent developments. Take the $\mathbb{F}_{2^{6120}}$ example: it clearly passes the field size criterion, but also the subgroup rule, as the group order $2^{6120} - 1$ has one $1536$-bit prime factor. Not all binary fields are affected equally, however. Both Göloğlu et al and ...

4

Göloğlu, Granger, McGuire, and Zumbrägel broke the DLP in the Galois finite field with $2^n$ elements for $n=6120$, and Antoine Joux did it for $n=6168$, with modest computing power. These recent announcements directly imply that cryptosystems (if any) based on the DLP in a field with $2^n$ elements are no longer secure, including for $n$ big enough that ...

3

Yes, an adversary can definitely decrypt a DES message, given sufficient funding. Fifteen years ago, in 1998, the EFF built a DES cracker (nicknamed Deep Crack) that can recover a DES key in a day. Today, anyone with the money can purchase a commercially available DES cracker named COPACOBANA. For RC2, I'm not aware of any practical attacks. (You still ...

2

They are generally relevant only to symmetric-key cryptography (e.g., block ciphers, hash functions, message authentication codes). There's no deep reason why -- it's just that differential and linear cryptanalysis tend to be effective against the sort of structure that are commonly used in block ciphers, but not very effective against the sort of designs ...

1

I am a master's student in cryptography, and I have had a few summers worth of experience in applied cryptography. Cryptography is a broad field, and there are many aspects to it. If you are looking at cryptography in academia, I would definitely recommend having a strong background in mathematics and computer science, and as strong a ...

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