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Aleksei Udovenko

@hellman@mathstodon.xyz

mastodon 4.7.2

Cryptography researcher, CTF player

White-box cryptography, symmetric-key cryptography, Boolean functions, cryptanalysis in general

267 Followers

79 Following

8 Posts

Joined November 01, 2022

Blog:

https://affine.group

Github:

https://github.com/hellman

Bluesky:

https://helllman.bsky.social

Aleksei Udovenko @hellman@mathstodon.xyz

· 5mo ago

Our paper https://ia.cr/2026/913 shows how to find affine maps agreeing with an S-box on as many as possible inputs. Look for presentation at #Eurocrypt 2026 today!

The code is already available. Also check out a vide-coded interactive tool, it's fun to play with: https://affine.group/pages/greedy-extension

ia.cr

Aleksei Udovenko @hellman@mathstodon.xyz

· 5mo ago

Our paper about cryptanalysis of AIM2 is on the front page of eprint 😀 Look for tomorrow's presentation at #Eurocrypt 2026. I will share more details later. https://ia.cr/2026/903

mathstodon.xyz

Aleksei Udovenko @hellman@mathstodon.xyz

· 5mo ago

Replying to

@christianp@mathstodon.xyz Most of the time a(n)=a(n-1)+n, so can be "compressed" by looking into those n where it does not hold. What is interesting, quite many of those actually belong to A395531 itself!

n =     3, in A395531? yes,   a(n)-a(n-1) = 4 = n + 1
n =     6, in A395531?  - ,   a(n)-a(n-1) = 9 = n + 3
n =    11, in A395531? yes,   a(n)-a(n-1) = 14 = n + 3
n =    16, in A395531? yes,   a(n)-a(n-1) = 20 = n + 4
n =    22, in A395531?  - ,   a(n)-a(n-1) = 30 = n + 8
n =    32, in A395531? yes,   a(n)-a(n-1) = 38 = n + 6
n =    40, in A395531? yes,   a(n)-a(n-1) = 47 = n + 7
n =    49, in A395531? yes,   a(n)-a(n-1) = 57 = n + 8
n =    59, in A395531? yes,   a(n)-a(n-1) = 68 = n + 9
n =    67, in A395531?  - ,   a(n)-a(n-1) = 70 = n + 3
n =    70, in A395531?  - ,   a(n)-a(n-1) = 80 = n + 10
n =    85, in A395531? yes,   a(n)-a(n-1) = 96 = n + 11
n =    98, in A395531? yes,   a(n)-a(n-1) = 110 = n + 12

https://gist.github.com/hellman/a4a56f013085edf379ac6377db0fa9bb

Gist

Bricks OEIS A395531

Bricks OEIS A395531. GitHub Gist: instantly share code, notes, and snippets.

Aleksei Udovenko @hellman@mathstodon.xyz

· 5mo ago

Replying to

@christianp@mathstodon.xyz Wow! This extra ≈n^0.5 term actually precisely matches the index of n in a(n), when it is in the sequence (which happens very often, as mentioned) ! 😮 So for these cases we get a(n) = n(n+3)/2 - a.index(n) See the updated gist https://gist.github.com/hellman/a4a56f013085edf379ac6377db0fa9bb

Gist

Bricks OEIS A395531

Bricks OEIS A395531. GitHub Gist: instantly share code, notes, and snippets.

Aleksei Udovenko @hellman@mathstodon.xyz

· 6mo ago

Replying to

oeis.org

A006863 - OEIS

Aleksei Udovenko @hellman@mathstodon.xyz

· 5mo ago

Replying to

@christianp@mathstodon.xyz Some larger values to show that it's still rare: ... n = 3632, in A395531? yes, a(n)-a(n-1) = 3715 = n + 83 n = 3656, in A395531? - , a(n)-a(n-1) = 3667 = n + 11 n = 3717, in A395531? - , a(n)-a(n-1) = 3801 = n + 84 n = 3814, in A395531? yes, a(n)-a(n-1) = 3899 = n + 85 n = 3901, in A395531? yes, a(n)-a(n-1) = 3987 = n + 86 n = 3989, in A395531? yes, a(n)-a(n-1) = 4076 = n + 87 n = 4078, in A395531? yes, a(n)-a(n-1) = 4166 = n + 88 n = 4168, in A395531? yes, a(n)-a(n-1) = 4257 = n + 89 n = 4259, in A395531? yes, a(n)-a(n-1) = 4349 = n + 90 n = 4351, in A395531? yes, a(n)-a(n-1) = 4442 = n + 91 n = 4444, in A395531? yes, a(n)-a(n-1) = 4536 = n + 92

Aleksei Udovenko @hellman@mathstodon.xyz

· 5mo ago

Replying to

@christianp@mathstodon.xyz Experimentally, asymptotically seems to be within a(n) = n(n+3)/2 - o(n^0.5 log(n)) The peaks of (a(n) - n(n+3)/2)/n^0.5 seem to continue slowly growing, not sure if converging. Checked up to a(21710)=235694408 .

Aleksei Udovenko @hellman@mathstodon.xyz

· 5mo ago

Replying to

@christianp@mathstodon.xyz This seems to happen always when n in a(n) (even if the diff matches n).