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A scalable algorithm for homomorphic computing on multi-core
ANBLIC project (ANalysis in BLInd Clouds) funded by FUI/BPI with ATOS Capgemini CoESSI Wallix CEA ENS UPEC BSP Execution of Homomorphic Programs 4 / 26
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IntroductionCingulataExecution BSPConclusion
A scalable algorithm for homomorphic
computing on multi-core clustersFrédéric Gava & Léa Bayati
Laboratory ofAlgorithms,Complexity andLogic (LACL)University of Paris-East
BSP Execution of Homomorphic Programs1 / 26
IntroductionCingulataExecution BSPConclusion
Outline
1Introduction
2Homomorphic programming
3BSP execution of boolean circuits
4Conclusion
BSP Execution of Homomorphic Programs2 / 26
IntroductionCingulataExecution BSPConclusion
Outline
1Introduction
2Homomorphic programming
3BSP execution of boolean circuits
4Conclusion
BSP Execution of Homomorphic Programs3 / 26
IntroductionCingulataExecution BSPConclusion
Q: What is the context?Too-curious-but-honestser ver(cloud pro vider):Personal
data ( e. g.medical; health pass)Compagny data (medical data orsecret f ormula) ANBLICproject (ANalysis inBLIndClouds), funded by FUI/BPI with ATOS, Capgemini, CoESSI, Wallix, CEA, ENS, UPECBSP Execution of Homomorphic Programs4 / 26
IntroductionCingulataExecution BSPConclusion
Q: What is the context?Too-curious-but-honestser ver(cloud pro vider):Personal
data ( e. g.medical; health pass)Compagny data (medical data orsecret f ormula) ANBLICproject (ANalysis inBLIndClouds), funded by FUI/BPI with ATOS, Capgemini, CoESSI, Wallix, CEA, ENS, UPECBSP Execution of Homomorphic Programs4 / 26
IntroductionCingulataExecution BSPConclusion
Q: What is the context?Too-curious-but-honestser ver(cloud pro vider):Personal
data ( e. g.medical; health pass)Compagny data (medical data orsecret f ormula) ANBLICproject (ANalysis inBLIndClouds), funded by FUI/BPI with ATOS, Capgemini, CoESSI, Wallix, CEA, ENS, UPECBSP Execution of Homomorphic Programs4 / 26
IntroductionCingulataExecution BSPConclusion
Q: More specifically?Q: What isf?Homomorphic programming iscomputationally univ ersalBut highly
inefficientBSP Execution of Homomorphic Programs5 / 26
IntroductionCingulataExecution BSPConclusion
Q: More specifically?Q: What isf?Homomorphic programming iscomputationally univ ersalBut highly
inefficientBSP Execution of Homomorphic Programs5 / 26
IntroductionCingulataExecution BSPConclusion
Q: What is homomorphic encryption?A homomorphic operator (;h)IfEncmiciandDeccimi(i"r1;2x)ThenDecc1hc2Decc1Decc2m1m2Fullyhomomor phicencr yption( FHE)FHEis when all the functions (Turing completness) can be
evaluated in a homomorphic way . Mainly, using boolean circuits multiplicative depth prob lem).BSP Execution of Homomorphic Programs6 / 26
IntroductionCingulataExecution BSPConclusion
Q: What is homomorphic encryption?A homomorphic operator (;h)IfEncmiciandDeccimi(i"r1;2x)ThenDecc1hc2Decc1Decc2m1m2Fullyhomomor phicencr yption( FHE)FHEis when all the functions (Turing completness) can be
evaluated in a homomorphic way . Mainly, using boolean circuits multiplicative depth prob lem).BSP Execution of Homomorphic Programs6 / 26
IntroductionCingulataExecution BSPConclusion
Q: Some examples?ClientCloudProblem and additional solutionProblem: very
inefficient prog rams(an e xamplelater) Solution: have executed them onHPCarchitectures(par alleland distributed ones) Needs of a bridging model (to scale and be portable) BSPBSP Execution of Homomorphic Programs7 / 26
IntroductionCingulataExecution BSPConclusion
Q: Some examples?ClientCloudProblem and additional solutionProblem: very
inefficient prog rams(an e xamplelater) Solution: have executed them onHPCarchitectures(par alleland distributed ones) Needs of a bridging model (to scale and be portable) BSPBSP Execution of Homomorphic Programs7 / 26
IntroductionCingulataExecution BSPConclusion
Q: Some examples?ClientCloudProblem and additional solutionProblem: very
inefficient prog rams(an e xamplelater) Solution: have executed them onHPCarchitectures(par alleland distributed ones) Needs of a bridging model (to scale and be portable) BSPBSP Execution of Homomorphic Programs7 / 26
IntroductionCingulataExecution BSPConclusion
Outline
1Introduction
2Homomorphic programming
3BSP execution of boolean circuits
4Conclusion
BSP Execution of Homomorphic Programs8 / 26
IntroductionCingulataExecution BSPConclusion
Q: How FHE programming?UsingCingulata (CEA)
https://github.com/CEA-LIST/Cingulata CingulataC++environmentCompilationchain (specific types ) C++operator overloadingcapabilities Generation of (encrypted)boolean circuitsBSP Execution of Homomorphic Programs9 / 26
IntroductionCingulataExecution BSPConclusion
Q: How FHE programming?UsingCingulata (CEA)
https://github.com/CEA-LIST/Cingulata CingulataC++environmentCompilationchain (specific types ) C++operator overloadingcapabilities Generation of (encrypted)boolean circuitsBSP Execution of Homomorphic Programs9 / 26
IntroductionCingulataExecution BSPConclusion
Q: Can you show a simple example?Sum of two integers !1#include <*.hxx>2intmain() {
3»»»»»»CiContext::set_config(...);//Set context
4»»»»»»5»»»»»»CiInta{ CiInt::u8};//create from unsigned 8- bittemplate
6»»»»»»CiIntb{ CiInt::u8};
7»»»»»»CiIntc{ CiInt::u8};
8»»»»»»9»»»»»»a.read("a");//read variable a and set name
10»»»»»»b.read("b");//read variable a and set name
11»»»»»»c = a + b ;
12»»»»»»c.write("c");//set name and write variable
13»»»»»»14»»»»»»/*Exportto file the " tracked"circuit */
15»»»»»»CiContext::get_bit_exec_t()>export_blif(blif_name, "hello");
16}BSP Execution of Homomorphic Programs10 / 26
IntroductionCingulataExecution BSPConclusion
Q: Can you show a simple example?Sum of two integers !1#include <*.hxx>2intmain() {
3»»»»»»CiContext::set_config(...);//Set context
4»»»»»»5»»»»»»CiInta{ CiInt::u8};//create from unsigned 8- bittemplate
6»»»»»»CiIntb{ CiInt::u8};
7»»»»»»CiIntc{ CiInt::u8};
8»»»»»»9»»»»»»a.read("a");//read variable a and set name
10»»»»»»b.read("b");//read variable a and set name
11»»»»»»c = a + b ;
12»»»»»»c.write("c");//set name and write variable
13»»»»»»14»»»»»»/*Exportto file the " tracked"circuit */
15»»»»»»CiContext::get_bit_exec_t()>export_blif(blif_name, "hello");
16}BSP Execution of Homomorphic Programs10 / 26
IntroductionCingulataExecution BSPConclusion
Q: Can you show a real example?Membership in an
encrypted data-base !1intmain() {2»»»»»»CiIntP assTarget{CiInt::s32};
3»»»»»»vector HeathPass(list_size,CiInt ::s32);
5»»»»»»//Initialising the Data Base ( reading)as an array
6»»»»»»for( inti = 0; i < list_siz e;i++) {
7»»»»»»»
»»»»»HeathPass[i].read("b_" + to_string(i));8»»»»»»}
9»»»»»»//Comparing all the data ( whileupdating the answer )
10»»»»»»boolans wer= f alse;
11»»»»»»for( inti = 0; (i < list_siz e)or ( not(answer)); i++) {
12»»»»»»»
»»»»»answer = (PassTarget == HeathPass[i]);13»»»»»»}
14»»»»»»//Finally writing the answer
16}Ho, goti!1intmain() {
2»»»»»»CiIntP assTarget{CiInt::s32};
3»»»»»»vector HeathPass(list_size,CiInt ::s32);
5»»»»»»//Initialising the Data Base ( reading)as an array
6»»»»»»for( inti = 0; i < list_siz e;i++) {
7»»»»»»»
»»»»»HeathPass[i].read("b_" + to_string(i));8»»»»»»}
9»»»»»»//Comparing all the data ( whileupdating the answer )
10»»»»»»CiBitans wer(0);
11»»»»»»for( inti = 0; i < list_siz e;i++) {
12»»»»»»»
»»»»»answer = answerxor (P assTarget== HeathP ass[i]);13»»»»»»}
14»»»»»»//Finally writing the answer
16}BSP Execution of Homomorphic Programs11 / 26
IntroductionCingulataExecution BSPConclusion
Q: Can you show a real example?Membership in an
encrypted data-base !1intmain() {2»»»»»»CiIntP assTarget{CiInt::s32};
3»»»»»»vector HeathPass(list_size,CiInt ::s32);
5»»»»»»//Initialising the Data Base ( reading)as an array
6»»»»»»for( inti = 0; i < list_siz e;i++) {
7»»»»»»»
»»»»»HeathPass[i].read("b_" + to_string(i));8»»»»»»}
9»»»»»»//Comparing all the data ( whileupdating the answer )
10»»»»»»boolans wer= f alse;
11»»»»»»for( inti = 0; (i < list_siz e)or ( not(answer)); i++) {
12»»»»»»»
»»»»»answer = (PassTarget == HeathPass[i]);13»»»»»»}
14»»»»»»//Finally writing the answer
16}Ho, goti!1intmain() {
2»»»»»»CiIntP assTarget{CiInt::s32};
3»»»»»»vector HeathPass(list_size,CiInt ::s32);
5»»»»»»//Initialising the Data Base ( reading)as an array
6»»»»»»for( inti = 0; i < list_siz e;i++) {
7»»»»»»»
»»»»»HeathPass[i].read("b_" + to_string(i));8»»»»»»}
9»»»»»»//Comparing all the data ( whileupdating the answer )
10»»»»»»CiBitans wer(0);
11»»»»»»for( inti = 0; i < list_siz e;i++) {
12»»»»»»»
»»»»»answer = answerxor (P assTarget== HeathP ass[i]);13»»»»»»}
14»»»»»»//Finally writing the answer
16}BSP Execution of Homomorphic Programs11 / 26
IntroductionCingulataExecution BSPConclusion
Q: Can you show a real example?Membership in an
encrypted data-base !1intmain() {2»»»»»»CiIntP assTarget{CiInt::s32};
3»»»»»»vector HeathPass(list_size,CiInt ::s32);
5»»»»»»//Initialising the Data Base ( reading)as an array
6»»»»»»for( inti = 0; i < list_siz e;i++) {
7»»»»»»»
»»»»»HeathPass[i].read("b_" + to_string(i));8»»»»»»}
9»»»»»»//Comparing all the data ( whileupdating the answer )
10»»»»»»boolans wer= f alse;
11»»»»»»for( inti = 0; (i < list_siz e)or ( not(answer)); i++) {
12»»»»»»»
»»»»»answer = (PassTarget == HeathPass[i]);13»»»»»»}
14»»»»»»//Finally writing the answer
16}Ho, goti!1intmain() {
2»»»»»»CiIntP assTarget{CiInt::s32};
3»»»»»»vector HeathPass(list_size,CiInt ::s32);
5»»»»»»//Initialising the Data Base ( reading)as an array
6»»»»»»for( inti = 0; i < list_siz e;i++) {
7»»»»»»»
»»»»»HeathPass[i].read("b_" + to_string(i));8»»»»»»}
9»»»»»»//Comparing all the data ( whileupdating the answer )
10»»»»»»CiBitans wer(0);
11»»»»»»for( inti = 0; i < list_siz e;i++) {
12»»»»»»»
»»»»»answer = answerxor (P assTarget== HeathP ass[i]);13»»»»»»}
14»»»»»»//Finally writing the answer
16}BSP Execution of Homomorphic Programs11 / 26
IntroductionCingulataExecution BSPConclusion
Q: Can you show a real example?Membership in an
encrypted data-base !1intmain() {2»»»»»»CiIntP assTarget{CiInt::s32};
3»»»»»»vector HeathPass(list_size,CiInt ::s32);
5»»»»»»//Initialising the Data Base ( reading)as an array
6»»»»»»for( inti = 0; i < list_siz e;i++) {
7»»»»»»»
»»»»»HeathPass[i].read("b_" + to_string(i));8»»»»»»}
9»»»»»»//Comparing all the data ( whileupdating the answer )
10»»»»»»boolans wer= f alse;
11»»»»»»for( inti = 0; (i < list_siz e)or ( not(answer)); i++) {
12»»»»»»»
»»»»»answer = (PassTarget == HeathPass[i]);13»»»»»»}
14»»»»»»//Finally writing the answer
16}Ho, goti!1intmain() {
2»»»»»»CiIntP assTarget{CiInt::s32};
3»»»»»»vector HeathPass(list_size,CiInt ::s32);
5»»»»»»//Initialising the Data Base ( reading)as an array
6»»»»»»for( inti = 0; i < list_siz e;i++) {
7»»»»»»»
»»»»»HeathPass[i].read("b_" + to_string(i));8»»»»»»}
9»»»»»»//Comparing all the data ( whileupdating the answer )
10»»»»»»CiBitans wer(0);
11»»»»»»for( inti = 0; i < list_siz e;i++) {
12»»»»»»»
»»»»»answer = answerxor (P assTarget== HeathP ass[i]);13»»»»»»}
14»»»»»»//Finally writing the answer
16}BSP Execution of Homomorphic Programs11 / 26
IntroductionCingulataExecution BSPConclusion
Q: So?What can we remark?
Cingulata
gener ates boolean circuitsThey are
big b utalso manipulating encr yptedbooleansMaking their execution very
slo wEven on
m ulti-cores using par allelthreadsWhat can we do?
Distributed
e xecutionusing the BSPmodelFinding adistr ibutionof the gatesBenchmarkingWhy not using?
Dynamic
schedulling (w orkflow):too long to redistribute dataMaster-slave: sameComplex
algor ithm(model) = loss of confidenceBSP Execution of Homomorphic Programs12 / 26
IntroductionCingulataExecution BSPConclusion
Q: So?What can we remark?
Cingulata
gener ates boolean circuitsThey are
big b utalso manipulating encr yptedbooleansMaking their execution very
slo wEven on
m ulti-cores using par allelthreadsWhat can we do?
Distributed
e xecutionusing the BSPmodelFinding adistr ibutionof the gatesBenchmarkingWhy not using?
Dynamic
schedulling (w orkflow):too long to redistribute dataMaster-slave: sameComplex
algor ithm(model) = loss of confidenceBSP Execution of Homomorphic Programs12 / 26
IntroductionCingulataExecution BSPConclusion
Q: So?What can we remark?
Cingulata
gener ates boolean circuitsThey are
big b utalso manipulating encr yptedbooleansMaking their execution very
slo wEven on
m ulti-cores using par allelthreadsWhat can we do?
Distributed
e xecutionusing the BSPmodelFinding adistr ibutionof the gatesquotesdbs_dbs5.pdfusesText_9[PDF] fui financement
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