Genetics in EACirc DESCRIPTION OF THE COMPONENTS BASED ON EVOLUTION

The overall picture o Circuit o The circuit is modified in an evolutionary way o Each circuit is evaluated how well it distinguishes true random data from tested data o The aim is to find such a circuit that is a good distinguisher EvaluateEvolve

Evaluation of a circuit (1) o Use the circuit to compute results for Test Vectors (TV) o TV = reference (true random) + test data (crypto output) o Number: 1 000x (frequently used) – x (optimal) TVs o Configurable in config file o Length (input): size of block of output (typically 16 bytes) o Configurable in config file o Length (output): 1 (typically used) – 4 bytes o Configurable in config file

Evaluation of a circuit (2) o Compute the results for all test vectors o Do it twice: true random data & tested data o You get a number (1 000x – x) of results (1-4 bytes) o Organize the results into categories o Make some resulting values equivalent o Calculate histogram o Evaluate whether the two histograms (random vs. tested) have the same distribution o Final result is a single P-value (float) which is our fitness

Circuit evaluation The result of the circuit evaluation if a single value in the form of a P-value or fitness (1 - P-value) TVs (True Random) 1000 results Histogram: 1000 TVs (Tested Data) 1000 results Histogram: Similar distribution? P-value

Circuit evolution (high level view) o The aim is to get such a circuit that is able to distinguish true random data from tested data o The smaller P-value the better o Circuit evolution o Set – perform a number of evolution steps o Typically 100 steps (configurable in config file) o For each set a new sequence of TVs is generated o After each set remember the P-value (tested with the new TVs) o After a number of generations analyze uniformity of p-values by a KS test o Generations: x – x (configurable in config file) o KS test – test if P-values are uniformly distributed o If KS < 0.01 then the distinguisher WORKS! (and we are happy)

Circuit evolution (high level view) 1 st Set 2 nd Set P-value 0 1 KS Total number of generations

Circuit description First layer Last layer Intermediate layers Input data (test vectors) Output data (results)

Circuit dimensions and arity of nodes o Width of a layer: typically 8 (configurable in config file) o Width of the last layer: typically 1 (must be between 1-4) o Total number of layers: typically 5 (configurable in config file) o Arity of nodes (we talk about node inputs here) o First layer: any number & any localization o Intermediate layers: maximum of 4 inputs (config file) & locality restriction o Last layer: any number & any localization

Nodes Inputs (each 1 byte long) Function + argument Output (1 byte long)

Node types o NOP o CONS: constant o AND o NAND: AND then NEGATION o OR o NOR: OR then NEGATION o NOT o SHIL: left shift o SHIR: right shift o ROTL: left rotation o ROTR: right rotation o EQ: equals o LT: less than o GT: greater then o LEQ: less or equal o GEQ: greater or equal o BSLC: bit selector o READ: read directly input (of circuit, not node) o JVM sim

Node mutation o Probability of mutation of a node o for each node do the following mutation with the probability of 0.05 (config file): 1.Add or remove a connection (within connection restrictions) 2.Change the node function (within restrictions in config file) 3.Change the node argument (no matter if function is using arg) o Result of the mutation is a valid individual

Crossover o Input: 2 circuits (chosen by a selection strategy) o Output: 1 or 2 circuits as a combination of the input circuits o Two types of crossover supported: o Horizontal (not used) o Vertical (typically used) o Nodes carry their connectors through the crossover

Circuit crossover - vertical

Circuit initialization o First layer o Connections: link each node with an input o Functions: XOR (+ random argument) o Intermediate layers o Connections: 0-4 (random, within the locality restrictions) o Functions and arguments: random o Last layer o Connections: 0-all (random) o Functions and arguments: random

Evolution o Currently used typical parameters o Population: 1 o Replacement size: 1 o Probability of crossover: 0 o Probability of mutation: 0.05 o The same for connections, functions and arguments

Genetics

Parent selection o Roulette selection strategy (typically used) o Take the candidates and spread them in the 0-1 interval o The better fitness of the candidate the larger section of the interval it occupies (not linear scale!) o Generate a random float from 0-1 interval o The candidate occupying the section with the random float wins

Replacement

EACirc