[Cryptography] mathematical constants

[Pierre Abbat]

On Sunday, June 7, 2026 8:57:53 PM EDT Peter Gutmann via cryptography wrote:
> The problem is that with any kind of famous irrational number you're mostly
> relying on people believing that the hex string you're using somehow
> corresponds to an encoding of Noodleheinz's Constant or whatever [0].  I'd
> go with either some well-known piece of text ("Friends, Romans,
> countrymen...") if low entropy is OK or the same thing run through HKDF if
> you need high entropy, that's pretty easy for anyone to verify.

The actual entropy in the byte sequence of an irrational constant is zero, 
except for Chaitin's constant. A very long sequence of bytes of the constant 
can be computed by a small program.

In the source code of Twistree, I put instructions in Haskell and Julia for 
computing exp(4) as a 2-adic number, using packages written by someone else. 
Each entry in the collection of constants could link to a program that 
computes the constant.

> [0] Has anyone ever verified things like the SHA-2 constants?  How are the
>     fractional parts of square/cube roots encoded to get the hex values?

To verify the hex value of a square root, square it. Verifying 0x9e3779b9:

julia> 0x09e3779b9^2
0x61c88645e35e67b1

julia> 0x11e3779b9^2
0x3ffffffee35e67b1

julia> UInt128(0x11e3779b9)^2
0x00000000000000013ffffffee35e67b1

Pierre

-- 
The Black Garden on the Mountain is not on the Black Mountain.