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Shamir Secret Sharing in Java

License

LGPL-2.1, LGPL-2.1 licenses found

Licenses found

LGPL-2.1
LICENSE
LGPL-2.1
license.txt
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reference-project/secretshare

 
 

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Java implementation of Shamir's Secret Sharing algorithmas described in Applied Cryptography [as LaGrange Interpolating Polynomial Scheme].

Table of contents

Dependencies

The following are required to run the application in secretshare.jar:

  1. jre 11 (LTS)

The following are used to compile the project:

  1. jdk 11 (LTS)
  2. gradlew (uses gradle 5.6.2)

The following are used to completely build and test the project:

  1. JUnit 4.xThis is needed for the (Unit and Integration) Test .java files to compile.

Note: the last version of this library to support jdk 1.6 (and jdk 8) was 1.4.4 - seeSecretShare 1.4.4 Release Tag orSecretShare 1.4.4 Maven Central. It is sad to let 1.6 go, but Java SE 6 was released in 2006, and EOL'd in 2013. Java SE 8 was released in 2014, and EOL'd in 2019/Jan.

Build

  1. Compile locally - build the project with gradlew (gradle wrapper)
    $ ./gradlew build  [creates build/libs/secretshare-1.4.4.jar]    $ cp build/libs/secretshare-1.4.4.jar ./secretshare.jar  [copies the .jar into the current directory]

Officially Released Artifact

  1. Use the artifact in your build - dependency information:
      group:   com.tiemens       name:   secretshare    version:   1.4.4

Central Repository -SecretShare 1.4.4 - to see dependency informationformatted for Maven, Ivy, Grape, Gradle, Buildr, etc.

Architecture Documentation

SeeArchitecture.md

Use

There are two main ways to use the application: split and combine.Split takes a secret (number or string) and splits it into 'n' shares.Combine takes 'k' of 'n' shares and re-creates the secret (number or string).

a. split - To display usage:

$ java -jar secretshare.jar split

b. combine - To display usage:

$ java -jar secretshare.jar combine

Examples of command line invocations

a. Create a share size 6 with threshold 3 with "Cat" as the secret string. Note: the low modulus of 16639793 limits the size of the secret number, which in turn limits the length of the secret string.
$ java -jar secretshare.jar split -k 3 -n 6 -m 16639793 -sS "Cat"
Sample output
Secret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : f8d4ec0b-f3e0-4946-af1c-6142477beb04n = 6k = 3modulus = 16639793modulus = bigintcs:fde731-829FB0Share (x:1) = 9140967Share (x:2) = 4154189Share (x:3) = 6095319Share (x:4) = 14964357Share (x:5) = 14121510Share (x:6) = 3566778Share (x:1) = bigintcs:8b7ae7-32F939Share (x:2) = bigintcs:3f634d-23AA55Share (x:3) = bigintcs:5d01d7-DB6BF4Share (x:4) = bigintcs:e45685-F8C8D8Share (x:5) = bigintcs:d77a26-22E9B6Share (x:6) = bigintcs:366cba-B203FC
b. Create a share size 6 with threshold 3 as above, but pipes the output of "split" to the input of "combine", which then re-creates the secret number and the secret string "Cat".
$ java -jar secretshare.jar split -k 3 -n 6 -m 16639793 -sS "Cat" \ | java -jar secretshare.jar combine -stdin
Sample output
Secret Share version 1.4.5-SNAPSHOTsecret.number = '4415860'secret.string = 'Cat'
c. Create a share size 6 with threshold 3 as above, but with a long secret string. Note: no modulus was given, so a pre-defined 384-bit prime was used as the modulus. The 384 bit prime allows 48 characters of secret string.
$ java -jar secretshare.jar split -k 3 -n 6 -sS "The Cat In The Hat"
Sample output
Secret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : 613a4311-e093-4ad3-af1a-fcc0d277ac03n = 6k = 3modulus = 83085671664126938805092614721037843700776366159998897420433674117190444262260240009907206384693584652377753448639527modulus = bigintcs:000002-1bd189-52959f-874f79-3d6cf5-11ac82-e6cea4-46c19c-5f523a-5318c7-e0f379-66f9e1-308c61-2d8d0b-dba253-6f54b0-ec6c27-3198DBShare (x:1) = 15979896060676809512661644548376824098571574Share (x:2) = 37851134048919502035795818694391308922347316Share (x:3) = 72966669768703432152038843640464501050126190Share (x:4) = 121326503220028599861390719386596400481908196Share (x:5) = 182930634402895005163851445932787007217693334Share (x:6) = 257779063317302648059421023279036321257481604Share (x:1) = bigintcs:b770b1-a12533-044603-85c735-15cdfe-23c536-334367Share (x:2) = bigintcs:000001-b2827c-516208-007f06-58d30f-cc5652-d75f34-FC877BShare (x:3) = bigintcs:000003-459dc5-30f9e0-68cb51-e743e4-8bfe1e-632f6e-741FFDShare (x:4) = bigintcs:000005-70c28c-3fecbc-3d2ae6-3119b3-54c560-c735e4-701AA3Share (x:5) = bigintcs:000008-33f0d1-7e3a9b-7d9dc3-36547c-26ac1a-037296-331AD8Share (x:6) = bigintcs:00000b-8f2894-ebe37e-2a23e8-f6f43f-01b24a-17e584-4FA6BF
d. Create the same share as above, then pipes the output of "split" into the input of "combine", which prints out the secret string.
$ java -jar secretshare.jar split -k 3 -n 6 -sS "The Cat In The Hat" \ | java -jar secretshare.jar combine -stdin
Sample output
Secret Share version 1.4.5-SNAPSHOTsecret.number = '7352955803975354582636321202421046578798964'secret.string = 'The Cat In The Hat'
e. Create the same share as above, but use a pre-defined 4096 bit prime modulus. The 4096 bit prime allows 512 characters of secret string.
$ java -jar secretshare.jar split -k 3 -n 6 -prime4096 \    -sS "The Cat In The Hat 4096bits"
Sample output
Secret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : 100b5d58-de91-4c07-a885-5f75e5221b7an = 6k = 3modulus = 16710222102610440107068043371465990121279427984758140486147735732543262527544919309581228990959960933454241707431028205407801175010972697716211777405621844447135311624699359973445785442150139493030849120189695139622021101430363403930757354949513385879948926539292859265140544779841897745831487644537568464106991023630108604575150490083044175049593271254925175508848427143088944400255558397883427448667101368958164663781091806630951947745404989962231943601603024661584134672986801498693341608816527553412312812319737861910590928243420749213395009469338508019541095885541890008803615972806597516557801530791875113872380904094611929773211709366081401737953645348323163171237010704282848106803127761278746182709924566001996544238514546167359724648214393784828708337709298145449348366148476664877596527269176552273043572304982318495803088033967414331004526063175049856118607130798717168809146278034477061142090096734446658190827333485703051687166399550428503452215571581604276048958396735937452791507228393997083495197879290548002853265127569910930648812921091549545147941972750158605112325079312039054825870573986374161254590876872367709717423642369650017374448020838615475035626771463864178105646732507808534977443900875333446450467047221modulus = bigintcs:100000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000735-4C590BShare (x:1) = 91752672387558663698721782356024071282508657852444695946742526970Share (x:2) = 204968951434685892719162234036593454023843227633551926647678380915Share (x:3) = 374372189180096726717873608206141372282215456071890313806913084126Share (x:4) = 599962385623791165694855904864667826057625343167459857424446636603Share (x:5) = 881739540765769209650109124012172815350072888920260557500279038346Share (x:6) = 1219703654606030858583633265648656340159558093330292414034410289355Share (x:1) = bigintcs:df09d4-054225-6fb1a8-688740-13ab72-143919-1810cf-281fc0-14f3fa-912D2DShare (x:2) = bigintcs:000001-f2407d-db3c5d-91a424-eae5dd-b49ed8-07ade1-a21d44-eddb72-152b73-AC902AShare (x:3) = bigintcs:000003-8e0c62-a23209-d9f7be-f53c2d-4b3f52-22bfcd-be5991-8a6978-6a1ade-BD8311Share (x:4) = bigintcs:000005-b26d82-5a232a-48ac76-878a2e-d78ce0-656edd-6cc5b4-fdc9d3-13c23b-0D6058Share (x:5) = bigintcs:000008-5f63dd-030fbe-ddc24b-a1cfe2-598782-cfbb10-ad61af-47fc82-12218a-6E1783Share (x:6) = bigintcs:00000b-94ef72-9cf7c7-99393e-440d47-d12f39-61a467-802d80-690185-6538cb-0E9BF8
f. Create the same share as above, but output in a manner better suited for physically splitting up the shares in order to give them out individually with all required information.
$ java -jar secretshare.jar split -k 3 -n 6 -prime4096 \    -sS "The Cat In The Hat 4096bits" -printIndiv
Sample output
Secret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : 776b3f86-e58a-4c2f-8c54-0d9ef2972bbfn = 6k = 3modulus = 16710222102610440107068043371465990121279427984758140486147735732543262527544919309581228990959960933454241707431028205407801175010972697716211777405621844447135311624699359973445785442150139493030849120189695139622021101430363403930757354949513385879948926539292859265140544779841897745831487644537568464106991023630108604575150490083044175049593271254925175508848427143088944400255558397883427448667101368958164663781091806630951947745404989962231943601603024661584134672986801498693341608816527553412312812319737861910590928243420749213395009469338508019541095885541890008803615972806597516557801530791875113872380904094611929773211709366081401737953645348323163171237010704282848106803127761278746182709924566001996544238514546167359724648214393784828708337709298145449348366148476664877596527269176552273043572304982318495803088033967414331004526063175049856118607130798717168809146278034477061142090096734446658190827333485703051687166399550428503452215571581604276048958396735937452791507228393997083495197879290548002853265127569910930648812921091549545147941972750158605112325079312039054825870573986374161254590876872367709717423642369650017374448020838615475035626771463864178105646732507808534977443900875333446450467047221modulus = bigintcs:100000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000735-4C590BShare (x:1) = 91752672387558663698721782356024071282508657852444695946742526970Share (x:1) = bigintcs:df09d4-054225-6fb1a8-688740-13ab72-143919-1810cf-281fc0-14f3fa-912D2D^LSecret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : 776b3f86-e58a-4c2f-8c54-0d9ef2972bbfn = 6k = 3modulus = 16710222102610440107068043371465990121279427984758140486147735732543262527544919309581228990959960933454241707431028205407801175010972697716211777405621844447135311624699359973445785442150139493030849120189695139622021101430363403930757354949513385879948926539292859265140544779841897745831487644537568464106991023630108604575150490083044175049593271254925175508848427143088944400255558397883427448667101368958164663781091806630951947745404989962231943601603024661584134672986801498693341608816527553412312812319737861910590928243420749213395009469338508019541095885541890008803615972806597516557801530791875113872380904094611929773211709366081401737953645348323163171237010704282848106803127761278746182709924566001996544238514546167359724648214393784828708337709298145449348366148476664877596527269176552273043572304982318495803088033967414331004526063175049856118607130798717168809146278034477061142090096734446658190827333485703051687166399550428503452215571581604276048958396735937452791507228393997083495197879290548002853265127569910930648812921091549545147941972750158605112325079312039054825870573986374161254590876872367709717423642369650017374448020838615475035626771463864178105646732507808534977443900875333446450467047221modulus = bigintcs:100000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000735-4C590BShare (x:2) = 204968951434685892719162234036593454023843227633551926647678380915Share (x:2) = bigintcs:000001-f2407d-db3c5d-91a424-eae5dd-b49ed8-07ade1-a21d44-eddb72-152b73-AC902A^LSecret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : 776b3f86-e58a-4c2f-8c54-0d9ef2972bbfn = 6k = 3modulus = 16710222102610440107068043371465990121279427984758140486147735732543262527544919309581228990959960933454241707431028205407801175010972697716211777405621844447135311624699359973445785442150139493030849120189695139622021101430363403930757354949513385879948926539292859265140544779841897745831487644537568464106991023630108604575150490083044175049593271254925175508848427143088944400255558397883427448667101368958164663781091806630951947745404989962231943601603024661584134672986801498693341608816527553412312812319737861910590928243420749213395009469338508019541095885541890008803615972806597516557801530791875113872380904094611929773211709366081401737953645348323163171237010704282848106803127761278746182709924566001996544238514546167359724648214393784828708337709298145449348366148476664877596527269176552273043572304982318495803088033967414331004526063175049856118607130798717168809146278034477061142090096734446658190827333485703051687166399550428503452215571581604276048958396735937452791507228393997083495197879290548002853265127569910930648812921091549545147941972750158605112325079312039054825870573986374161254590876872367709717423642369650017374448020838615475035626771463864178105646732507808534977443900875333446450467047221modulus = bigintcs:100000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000735-4C590BShare (x:3) = 374372189180096726717873608206141372282215456071890313806913084126Share (x:3) = bigintcs:000003-8e0c62-a23209-d9f7be-f53c2d-4b3f52-22bfcd-be5991-8a6978-6a1ade-BD8311^LSecret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : 776b3f86-e58a-4c2f-8c54-0d9ef2972bbfn = 6k = 3modulus = 16710222102610440107068043371465990121279427984758140486147735732543262527544919309581228990959960933454241707431028205407801175010972697716211777405621844447135311624699359973445785442150139493030849120189695139622021101430363403930757354949513385879948926539292859265140544779841897745831487644537568464106991023630108604575150490083044175049593271254925175508848427143088944400255558397883427448667101368958164663781091806630951947745404989962231943601603024661584134672986801498693341608816527553412312812319737861910590928243420749213395009469338508019541095885541890008803615972806597516557801530791875113872380904094611929773211709366081401737953645348323163171237010704282848106803127761278746182709924566001996544238514546167359724648214393784828708337709298145449348366148476664877596527269176552273043572304982318495803088033967414331004526063175049856118607130798717168809146278034477061142090096734446658190827333485703051687166399550428503452215571581604276048958396735937452791507228393997083495197879290548002853265127569910930648812921091549545147941972750158605112325079312039054825870573986374161254590876872367709717423642369650017374448020838615475035626771463864178105646732507808534977443900875333446450467047221modulus = bigintcs:100000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000735-4C590BShare (x:4) = 599962385623791165694855904864667826057625343167459857424446636603Share (x:4) = bigintcs:000005-b26d82-5a232a-48ac76-878a2e-d78ce0-656edd-6cc5b4-fdc9d3-13c23b-0D6058^LSecret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : 776b3f86-e58a-4c2f-8c54-0d9ef2972bbfn = 6k = 3modulus = 16710222102610440107068043371465990121279427984758140486147735732543262527544919309581228990959960933454241707431028205407801175010972697716211777405621844447135311624699359973445785442150139493030849120189695139622021101430363403930757354949513385879948926539292859265140544779841897745831487644537568464106991023630108604575150490083044175049593271254925175508848427143088944400255558397883427448667101368958164663781091806630951947745404989962231943601603024661584134672986801498693341608816527553412312812319737861910590928243420749213395009469338508019541095885541890008803615972806597516557801530791875113872380904094611929773211709366081401737953645348323163171237010704282848106803127761278746182709924566001996544238514546167359724648214393784828708337709298145449348366148476664877596527269176552273043572304982318495803088033967414331004526063175049856118607130798717168809146278034477061142090096734446658190827333485703051687166399550428503452215571581604276048958396735937452791507228393997083495197879290548002853265127569910930648812921091549545147941972750158605112325079312039054825870573986374161254590876872367709717423642369650017374448020838615475035626771463864178105646732507808534977443900875333446450467047221modulus = bigintcs:100000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000735-4C590BShare (x:5) = 881739540765769209650109124012172815350072888920260557500279038346Share (x:5) = bigintcs:000008-5f63dd-030fbe-ddc24b-a1cfe2-598782-cfbb10-ad61af-47fc82-12218a-6E1783^LSecret Share version 1.4.5-SNAPSHOTDate                          : 2019-11-17 19:50:36UUID                          : 776b3f86-e58a-4c2f-8c54-0d9ef2972bbfn = 6k = 3modulus = 16710222102610440107068043371465990121279427984758140486147735732543262527544919309581228990959960933454241707431028205407801175010972697716211777405621844447135311624699359973445785442150139493030849120189695139622021101430363403930757354949513385879948926539292859265140544779841897745831487644537568464106991023630108604575150490083044175049593271254925175508848427143088944400255558397883427448667101368958164663781091806630951947745404989962231943601603024661584134672986801498693341608816527553412312812319737861910590928243420749213395009469338508019541095885541890008803615972806597516557801530791875113872380904094611929773211709366081401737953645348323163171237010704282848106803127761278746182709924566001996544238514546167359724648214393784828708337709298145449348366148476664877596527269176552273043572304982318495803088033967414331004526063175049856118607130798717168809146278034477061142090096734446658190827333485703051687166399550428503452215571581604276048958396735937452791507228393997083495197879290548002853265127569910930648812921091549545147941972750158605112325079312039054825870573986374161254590876872367709717423642369650017374448020838615475035626771463864178105646732507808534977443900875333446450467047221modulus = bigintcs:100000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000735-4C590BShare (x:6) = 1219703654606030858583633265648656340159558093330292414034410289355Share (x:6) = bigintcs:00000b-94ef72-9cf7c7-99393e-440d47-d12f39-61a467-802d80-690185-6538cb-0E9BF8
g. Combine 3 shares to recreate the original secret. Note: it is important that the -prime argument is specified before -s arguments.
$ java -jar secretshare.jar combine -k 3 -prime384 \    -s2 37851134048919502035795818694391308922347316 \    -s4 121326503220028599861390719386596400481908196 \    -s5 182930634402895005163851445932787007217693334
Sample output
Secret Share version 1.4.5-SNAPSHOTsecret.number = '7352955803975354582636321202421046578798964'secret.string = 'The Cat In The Hat'
h. Combine 4 shares, 3 good and 1 bad, using paranoid combination option.
$ java -jar secretshare.jar combine -k 3 -prime384 \    -paranoid 4 \    -s2 1882356874773438980155973947620693982153929916 \    -s3 12345678912345678912345678912345678 \    -s4 1882357204724127580025723830249209987221192644 \    -s5 1882357444072759374568880025530775541595539408
Sample output
Secret Share version 1.4.5-SNAPSHOTsecret.number = nullsecret.string = nullparanoid.totalAvailable = 4paranoid.allowedCount = 4paranoid.count = 4paranoid.summary = Disagreement (4 different answers)combine.1 = x1 = 83085671664126938805092614721037843700776366159998897420433674117190427321046833708006542535573073222337983827443095 - (validUTF8=false) = '^B^[\321\211R\357\277\275\357\277\275\357\277\Oy=l\357\277\275^Q\357\277\275\357\277\275\357\277\275\316\244F\357\277\275\357\277\275_R:S^X\357\277\275\357\277\275\357\277\275\357\277\275\357\277\275b=\357\277\275j\357\277\275\357\277\275{\357\277\275\357\277\275r\357\277\275\357\277\275^Z^P\357\277\275}\357\277\275'combine.2 = x1 = 16941212862714251189714249745173028423288392004 - (validUTF8=false) = '^B\357\277\275\357\277\275\357\277\275]\357\277\275O\357\277\275^FgT\357\277\275&\357\277\275\357\277\275\312\211D'combine.3 = x1 = 11294141817878225880787021369072517057803460598 - (validUTF8=false) = '^A\357\277\275rc\357\277\275\357\277\275\357\277\275\357\277\275\357\277\275 \311\240>\357\277\275a\357\277\275{\357\277\275^_\357\277\275'combine.4 = x1 = 1882356743151517032574974075571664781995241588 - (validUTF8=true) = 'TheKeyUsedToEncrypt'
i. Combine shares, showing examples for the -paranoid argument. Control how many extra combines to run (110), how many to print (4), and stop when an answer has been seen at least this many times (30). Use the -paranoid option if you (1) have extra shares and (2) some of your shares are corrupt.
$ java -jar secretshare.jar combine -k 3 -m 16639793 \    -paranoid 110,limitPrint=4,stopCombiningWhenAnyCount=30 \    -s1 7210616 -s2 11715382 -s3 4444444 -s4 9215151 -s5 2210154 \    -s6 13554960 -s7 9969983 -s8 8095016 -s9 7654321 -s10 1234567
Sample output
Secret Share version 1.4.5-SNAPSHOTsecret.number = nullsecret.string = nullparanoid.totalAvailable = 120paranoid.allowedCount = 110paranoid.count = 92paranoid.summary = Disagreement (60 different answers)combine.1 = x30 = 4415860 - (validUTF8=true) = 'Cat'combine.2 = x3 = 4140122 - (validUTF8=true) = '?,Z'combine.3 = x2 = 269137 - (validUTF8=true) = '^D^[Q'combine.4 = x1 = 16592886 - (validUTF8=false) = '^@\357\277\275\/\357\277\275'
j. Print information about Secret Share, including version, 192 bit, 384 bit, 4096 bit and 8192 bit primes.
$ java -jar secretshare.jar info
Sample output
Secret Share version 1.4.5-SNAPSHOTModulus 192 bits = 14976407493557531125525728362448106789840013430353915016137Modulus 192 bits = bigintcs:000002-62c8fd-6ec81b-3c0584-136789-80ad34-9269af-da237f-8ff3c9-12BCCDModulus 384 bits = 83085671664126938805092614721037843700776366159998897420433674117190444262260240009907206384693584652377753448639527Modulus 384 bits = bigintcs:000002-1bd189-52959f-874f79-3d6cf5-11ac82-e6cea4-46c19c-5f523a-5318c7-e0f379-66f9e1-308c61-2d8d0b-dba253-6f54b0-ec6c27-3198DBModulus 4096 bits = 16710222102610440107068043371465990121279427984758140486147735732543262527544919309581228990959960933454241707431028205407801175010972697716211777405621844447135311624699359973445785442150139493030849120189695139622021101430363403930757354949513385879948926539292859265140544779841897745831487644537568464106991023630108604575150490083044175049593271254925175508848427143088944400255558397883427448667101368958164663781091806630951947745404989962231943601603024661584134672986801498693341608816527553412312812319737861910590928243420749213395009469338508019541095885541890008803615972806597516557801530791875113872380904094611929773211709366081401737953645348323163171237010704282848106803127761278746182709924566001996544238514546167359724648214393784828708337709298145449348366148476664877596527269176552273043572304982318495803088033967414331004526063175049856118607130798717168809146278034477061142090096734446658190827333485703051687166399550428503452215571581604276048958396735937452791507228393997083495197879290548002853265127569910930648812921091549545147941972750158605112325079312039054825870573986374161254590876872367709717423642369650017374448020838615475035626771463864178105646732507808534977443900875333446450467047221Modulus 4096 bits = bigintcs:100000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000735-4C590BModulus 8192 bits = 279231522718570477942523966651848412786755625471035569262549193264568660953374539575363644038451708729333066699816198469916126929965359120284410819859854028564200012503601405321884115258380340520882394013079459378373602954907987087391050381798882893060582464649164778803202580377606793174221031756238305523801728417330041767401217359965327363800941065035149118936045803200708786247512086542238084017753586024109523236048614557723115585648257171971411582352854028094056289905359934753668545924906214201949630392942663006227207072738059572864458946995442098987135298017199066044684799206646046852007692829583685501822083927579071735457164040393298305467092078136746232403045411490624416360836139009389471599615055083953010222383976037199530343650749295317216621610856318814974339038401628152419869957586845887861406968283393603484693172919144488209043235143942917711597456617030850345093344845985897228637329601259767634683509551299437410250309746800132742906307824914615196564591280851829591037942122046141801113374061071502459843521616519068508840608866142367016446371333344905644939606218218417724015092650576657942326665080385451599873057465726933634139504551380207635732730508948201719784282311694063519119639243736364276253689069434848647101071362100254351086081223103674307034576258686423188956569254966171125838939239921106224566793694393912187263674266535325772507180754537736572272329042950336363370798851143956021690701705567437971039256378548127430749169994462670402156122918017938186142563187105245902896325033680839207188324653847844773975235005076945808128766572234433268495689937486958100390065467437864644075017104695336221543165982790695835615515631994231511431260924853427059238919995356824115989937622769832207704636596283910866202357492467506454291595823775435851401331614913666393860839942086098314120390709421306518971383380559076685994283375663380057764241494257799693167997775692501598019901080423655494004717753331078458159262055518170817180281440517060614547611105545747781301175793208826135138672277976088445981721562249959417511860209657110039278232822620356487671024234137135540726721167743323091920287701321960015105097732434284751017974443861383170363586137823503261214393288044057973810845631331034904805398832430192982926982354654090524982435531180945318487132920328174085989844087121548092990523399171888560553067218681856208752028326977093161880486624111065893663542842180250983316936056087246483576051350441471279745450361783242982069Modulus 8192 bits = bigintcs:010000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-0002b5-1E18FD

A complete scenario

  # Encrypt the PAYLOAD.$ cat PAYLOAD.txt   This is the PAYLOAD   Generated Wed May  9 19:58:01 CDT 2018   It has spaces at the front of every line$ openssl enc -pass pass:TheKeyUsedToEncrypt -aes-256-cbc -salt \              -in PAYLOAD.txt -out PAYLOAD.enc$ ls -l PAYLOAD.enc-rw-r--r--  1 timtiemens  users   128 May  9 19:58 PAYLOAD.enc  # Create the shares from the key.  # Use '-printIndiv' to make it easier to distribute the shares.$ PRINT=-printIndiv  # For this example, we'll print them all together$ PRINT=-printOne$ java -jar secretshare.jar split -k 3 -n 6 -sS "TheKeyUsedToEncrypt" $PRINTSecret Share version 1.4.4Date                          : 2018-05-09 19:59:55UUID                          : 5c1ed0de-b281-49db-890c-4fc12321775an = 6k = 3modulus = 83085671664126938805092614721037843700776366159998897420433674117190444262260240009907206384693584652377753448639527modulus = bigintcs:000002-1bd189-52959f-874f79-3d6cf5-11ac82-e6cea4-46c19c-5f523a-5318c7-e0f379-66f9e1-308c61-2d8d0b-dba253-6f54b0-ec6c27-3198DBShare (x:1) = 5029843236858503316023507982074352651731277871Share (x:2) = 11756782766980296102287198955234016324659726464Share (x:3) = 22063175333516895391366046995050655800780587367Share (x:4) = 35949020936468301183260052101524271080093860580Share (x:5) = 53414319575834513477969214274654862162599546103Share (x:6) = 74459071251615532275493533514442429048297643936Share (x:1) = bigintcs:0000e1-8bc4c6-aff0f0-47d7e4-9c63f3-dceb5a-05182f-086F30Share (x:2) = bigintcs:00020f-313f50-ea5144-91be7f-eb359a-28850f-c84880-A92812Share (x:3) = bigintcs:0003dd-58d4ea-149a52-511936-40e438-513093-c30167-AC7697Share (x:4) = bigintcs:00064c-028592-2ecc19-85e807-9d6fce-56ede5-f542e4-391126Share (x:5) = bigintcs:00095b-2e5149-38e69a-302af4-00d85c-39bd06-5f0cf7-80574AShare (x:6) = bigintcs:000d0a-dc380f-32e9d4-4fe1fb-6b1de1-f99df5-005fa0-4C058A  # Give the keys x:1, x:2, x:3, x:4, x:5 and x:6 away.  # Give the file PAYLOAD.enc away, or publish it somewhere public.  #  time passes   # Later, somebody acquires 3 shares - for example, x:2, x:4 and x:5 -  #  and then does this: $ java -jar secretshare.jar combine -k 3 \   -s2 11756782766980296102287198955234016324659726464 \   -s4 35949020936468301183260052101524271080093860580 \   -s5 53414319575834513477969214274654862162599546103Secret Share version 1.4.4secret.number = '1882356743151517032574974075571664781995241588'secret.string = 'TheKeyUsedToEncrypt'  # Then, using PAYLOAD.enc and the secret.string, recovers the secret PAYLOAD:$ openssl enc -d -pass pass:TheKeyUsedToEncrypt -aes-256-cbc \              -in PAYLOAD.enc -out RECOVER.txt$ cmp PAYLOAD.txt RECOVER.txt $ cat RECOVER.txt   This is the PAYLOAD   Generated Wed May  9 19:58:01 CDT 2018   It has spaces at the front of every line

Note on the Modulus

Using a shared modulus is ok - the modulus is NOT secret.You can use a randomly generated prime modulus if you'd like.It just takes longer.

Timing difference:                             Time To Generate Splita) using -prime4096 on 512-character secret    ==    0.3 secondsb) using -primeN    on 512-character secret    ==   57.1 seconds

Note on the size of 'k'

N.B.: 'split' is perfectly capable of generating k=100, k=200, even k=1000in a reasonable amount of time (k=1000 took 35 seconds).Note, however, that for some values of k, you will never [asa matter of practice] be able to recover the original secretfrom the shares with the secretshare.jar application.For k=1000, perhaps a super computer clustercould solve the matrix and recreate the original secret. Maybe.

SIMPLEX SOLVER (versions 1.4.2 and later)

ksecondsminutesyears
k = 220 seconds
k = 230 seconds
k = 240 seconds
k = 280 seconds
k = 290 seconds
k = 300.44 seconds
k = 502 seconds
k = 755 seconds
k = 9512 seconds
k = 13047 seconds
k = 180180 seconds
k = 230623 seconds
k = 2801662 seconds28 minutes
k = 650--1 year
k = 1000346276986880 seconds-11,000 years

The formula is roughly "4 times longer for each +50 in k".For k greater than 280, all times are calculated.
k=280 is the last "measured".So, k=280 is a pretty good practical limit, or k=95 for "immediate" results.

N.B.: Earlier versions of secretshare (1.4.1 and earlier) used a veryinefficient solving algorithm. For these versions, your "k" isin effect limited to less than k=30, and is probably more like k=20.

ORIGINAL SOLVER (versions 1.4.1 and earlier)Value 'k' versus recorded runtimes to complete the "combine" operation:
ksecondsminuteshoursdays
k = 193 seconds
k = 2010 seconds
k = 2139 seconds
k = 22156 seconds
k = 23646 seconds
k = 242460 seconds41 minutes
k = 25164 minutes
k = 26656 minutes11 hours
k = 2744 hours
k = 28176 hours7.3 days
k = 2930 days
k = 30120 days

The formula is roughly 10 * 4^(k - 20) seconds.For k greather than 25, all times are calculated.k=24 is the last "measured".For k = 90, that works out to be = 10 * 4^(90 - 20) = 1E42 seconds.Since a year has ~3E7 seconds, that will never happen.So, k=25 is a pretty good practical limit, or k=20 for "immediate" results.

Additional Documentation

Original Sourceforge Secret Sharing in Java - original SCM location. Out-of-date.

Resources - more links to useful Shamir Secret Share documentation and projects

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