“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 [...]

“Finite Field Arithmetic” Regrind into Keccak-V Format.

The long-promised Keccak-V regrind of the current FFA codebase appears below:

Title
VPatch
Seal

“Chapter 1: Genesis.”
ffa_ch1_genesis.kv.vpatch
ffa_ch1_genesis.kv.vpatch.asciilifeform.sig

“Chapter 2: Logical and Bitwise Operations.”
ffa_ch2_logicals.kv.vpatch
ffa_ch2_logicals.kv.vpatch.asciilifeform.sig

“Chapter 3: Shifts.”
ffa_ch3_shifts.kv.vpatch
ffa_ch3_shifts.kv.vpatch.asciilifeform.sig

“Chapter 4: Interlude: FFACalc.”
ffa_ch4_ffacalc.kv.vpatch
ffa_ch4_ffacalc.kv.vpatch.asciilifeform.sig

“Chapter 5: “Egyptological” Multiplication and Division.”
ffa_ch5_egypt.kv.vpatch
ffa_ch5_egypt.kv.vpatch.asciilifeform.sig

Chapter 6: “Geological” RSA.
ffa_ch6_simplest_rsa.kv.vpatch
ffa_ch6_simplest_rsa.kv.vpatch.asciilifeform.sig

Chapter 7: “Turbo Egyptians.”
ffa_ch7_turbo_egyptians.kv.vpatch
ffa_ch7_turbo_egyptians.kv.vpatch.asciilifeform.sig

Chapter 8: Interlude: Randomism.
ffa_ch8_randomism.kv.vpatch
ffa_ch8_randomism.kv.vpatch.asciilifeform.sig

Chapter 9: “Exodus from Egypt” with Comba’s Algorithm.
ffa_ch9_exodus.kv.vpatch
ffa_ch9_exodus.kv.vpatch.asciilifeform.sig

Chapter 10: Introducing Karatsuba’s Multiplication.
ffa_ch10_karatsuba.kv.vpatch
ffa_ch10_karatsuba.kv.vpatch.asciilifeform.sig

Chapter 11: Tuning and Unified API.
ffa_ch11_tuning_and_api.kv.vpatch
ffa_ch11_tuning_and_api.kv.vpatch.asciilifeform.sig

These, and all [...]

“Finite Field Arithmetic” Projected Release Timeline.

Several of my readers recently let me know (privately and in the Forum) that they are ready to pioneer the battlefield use of FFA. However they all have one question, “When the hell will be the beta release? And just how much spade work remains, and where?”

And so I have written this projection, [...]

Posted in: FFA, Friends, Progress by Stanislav 1 Comment

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)
[...]

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