“Finite Field Arithmetic.” Chapter 14A: Barrett’s Modular Reduction. (Part 1 of 2)

This article is part of a series of hands-on tutorials introducing FFA, or the Finite Field Arithmetic library. FFA differs from the typical “Open Sores” abomination, in that — rather than trusting the author blindly with their lives — prospective users are expected to read and fully understand every single line. In exactly the same [...]

“Finite Field Arithmetic.” Chapter 13: “Width-Measure” and “Quiet Shifts.”

This article is part of a series of hands-on tutorials introducing FFA, or the Finite Field Arithmetic library. FFA differs from the typical “Open Sores” abomination, in that — rather than trusting the author blindly with their lives — prospective users are expected to read and fully understand every single line. In exactly the same [...]

“Finite Field Arithmetic.” Chapter 12B: Karatsuba Redux. (Part 2 of 2)

This article is part of a series of hands-on tutorials introducing FFA, or the Finite Field Arithmetic library. FFA differs from the typical “Open Sores” abomination, in that — rather than trusting the author blindly with their lives — prospective users are expected to read and fully understand every single line. In exactly the same [...]

“Finite Field Arithmetic.” Chapter 12A: Karatsuba Redux. (Part 1 of 2)

This article is part of a series of hands-on tutorials introducing FFA, or the Finite Field Arithmetic library. FFA differs from the typical “Open Sores” abomination, in that — rather than trusting the author blindly with their lives — prospective users are expected to read and fully understand every single line. In exactly the same [...]

Hypertext Concordance for “Finite Field Arithmetic.”

In addition to phf’s excellent vpatch viewer, there will now be a page, generated via gnathtml, to help the interested reader to explore the moving parts of FFA.

Click here to view Ch.11, with ffa_calc.adb as the root node.

All subsequent chapters will also be offered in this reader-friendly format, in addition to the usual raw vpatch [...]

The Serpent Cipher’s Key Schedule Transform is Injective.

This article is a continuation of the previous, and concludes the series.

Let’s try this somewhat different variant of the program, which represents recurring bits of the expansion symbolically (and in a slightly more readable form) [...]

The Serpent Cipher’s Key Schedule Equation System, in Graphical Form.

This article is a continuation of the dig into the key schedule of the Serpent cipher.

For clarity, we will omit the routines already given in the previous article.

Let’s visualize the Serpent [...]

Serpent Cipher’s Key Schedule in Algebraic Form: with Reduction.

This article is a continuation of the recent mega-puzzler concerning the experiment.

This variant will reduce the equations. We will omit printing the input matrix, for brevity. And so:

;; Register bitness.
(defconstant +bitness+ 32)
 
(defun flatten (l)
[...]

Terms -8…8 of the Serpent Cipher’s Key Schedule in Algebraic Form.

This article is a byproduct of the recent mega-puzzler concerning the Serpent cipher’s key expansion procedure.

Behold:

;; Register bitness.
(defconstant +bitness+ 32)
 
(defun make-reg (reg-name bitness)
"Make algebraic representation of a register (bits in descending majority)"
(loop for i from [...]

Serpent in ICE40, Part 2.

This article is a continuation of “Can the Serpent Cipher fit in the ICE40 FPGA?”.

Below is a revision of the forward S-box of Serpent from the previous article, with all of the S-Box equations rewritten in the same form, [...]

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