“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 […]

“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, to […]

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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 […]

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) : ;; Register bitness. (defconstant +bitness+ 32)   (defun make-reg (reg-name bitness) "Make algebraic representation of a register (bits […]

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 key schedule as a graphic: ;; 256bit(key)+1(const) x 4224(132*32) matrix, last column for constant subterms (defvar *matrix* (make-array ‘(257 4224) :element-type ‘(mod […]