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 […]

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) "Flatten a tree." (cond ((null l) nil) ((atom l) (list l)) (t (mapcan #’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 (1- bitness) downto 0 collect (make-symbol (format nil "~A~A" reg-name i))))   (defun […]

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, i.e. using strictly AND, OR, and NOT operations, with none having more than six subclauses, […]

Can the Serpent Cipher fit in the ICE40 FPGA?

Current Table of Contents: The question of whether the Serpent cipher could fit in a ICE40 FPGA was posed recently, and my first thought was: why not bake what appears to be the heaviest moving part, and see how many gates it requires? Then it will be possible to estimate whether the entire thing is […]