sample-linear-distribution.md

The sample_linear_distribution executable

Synopsis

Synopsis: sample_linear_distribution <distribution> [ <n> ]

Samples a linear distribution.

The samples are written to the console.

Mandatory command line arguments

An argument <distribution> where

• <distribution> is the path to the distribution

Optional command line arguments

An optional argument specifying the number of samples (defaults to 1000):

• <n> sets the number of samples to <n>

Interpreting the output

For linear distributions tailored to solving discrete logarithm problems, the console output contains samples on the format

$ ./sample_linear_distribution distributions/linear-distribution-det-dim-2048-d-m-2048-s-30.txt
Importing the distribution from "distributions/linear-distribution-det-dim-2048-d-m-2048-s-30.txt"...
sample: 1 / 1000
alpha_d: -30263372532019227341001514356858773160022660210434384678669937624141261514061019381731890274754327471709730593595401768801655335660905945603920394945125329860471535383791849616922409101172135421789330230338349577720233711777215810848441636227829927071010939872485976769186622651390915384669292444506554135762103194301944833578707372688978003821275141132546255128324628286698836401230685446710313335145327236924292728743815338060002629397964419731865339165067945774384008375942786903423743878610114701035844100769584936015653110439015280612437770373692425904746584649164353152039539413431554423762071978256659262337523
j: 4556552578884873745478583197517193709590307264706689705308010029160963674379033156890351633096546936250171123369203734744799946229495028001955960033481310307823887356478155381889583864466553665812233238826362527926771218459167852184788588902397284820079505619819974675708571392748986770555075719343326714829752203792070507773697426194801651945860787741772205765143609234972159711894004870269697018863133524926311834862671803840202796004748475374186847203086543177204793974152915247195670325802425611472215586678025670377382470919376782019524173704247258956531577687479571109513381860472655148172238039571577043094493017201241514989736343
k: 107378028159679875945

(..)

where

• $\alpha_d$ is the admissible argument sampled
• $(j, k)$ is an integer pair sampled from the set of all integer pairs having argument $\alpha_d$

For linear distributions tailored to solving order-finding problems, the console output contains samples on the format

$ ./sample_linear_distribution distributions/linear-distribution-det-dim-2048-r-m-2048-s-30.txt
Importing the distribution from "distributions/linear-distribution-det-dim-2048-r-m-2048-s-30.txt"...
sample: 1 / 1000
alpha_r: -6664345951355689436648789223550246560443716959866939818778632515616470357969046968805977173908510303167769745267804928229333423879257946381953020640840464921822719737563844607651488139242001689455089239097828401647777487571729504127820391947200764955362972341107871058522887792224647393481848685042721525685101839683806986246985203758702991136342561252178096073342861912171899363413195815545554912977926778882107354566037012597638660710445390446357242446793790012423825423924838346083923218955141352188264193386873656039608557954866823189453397716091991537402761848797962466853450852288237645099729084334990928433660
j: 10366095817842715380235284668329444594561368081797017179617405633038810339775279559156100883543282224357285445282768351227270444934616863765278709928244083805917529037165967986686161224149539288463628403690838846596491863402640294697994213085186626129567824124617522644229753166825970573958503701214785795513177807494973181817287545551015744155843319424408866198013291250036346105692286471369806541765356417005869474867370824007566263295373184664596084613766434745316388914995193060598350422903608098795872525287598093630968412106320946145588244843762789965003279710359048178822375060187800154774979820919202754956578003901813096408560647

(..)

where

• $\alpha_r$ is the admissible argument sampled, and
• $j$ is an integer sampled from the set of all integers having argument $\alpha_r$.