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A scalable algorithm for homomorphic computing on multi-core

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IntroductionCingulataExecution BSPConclusion

A scalable algorithm for homomorphic

computing on multi-core clusters

Frédéric 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, UPEC

BSP 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, UPEC

BSP 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, UPEC

BSP Execution of Homomorphic Programs4 / 26

IntroductionCingulataExecution BSPConclusion

Q: More specifically?Q: What isf?Homomorphic programming iscomputationally univ ersal

But highly

inefficient

BSP Execution of Homomorphic Programs5 / 26

IntroductionCingulataExecution BSPConclusion

Q: More specifically?Q: What isf?Homomorphic programming iscomputationally univ ersal

But highly

inefficient

BSP 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 solution

Problem: 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) BSP

BSP Execution of Homomorphic Programs7 / 26

IntroductionCingulataExecution BSPConclusion

Q: Some examples?ClientCloudProblem and additional solution

Problem: 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) BSP

BSP Execution of Homomorphic Programs7 / 26

IntroductionCingulataExecution BSPConclusion

Q: Some examples?ClientCloudProblem and additional solution

Problem: 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) BSP

BSP 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 circuits

BSP 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 circuits

BSP 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 circuits

They are

big b utalso manipulating encr yptedbooleans

Making their execution very

slo w

Even on

m ulti-cores using par allelthreads

What can we do?

Distributed

e xecutionusing the BSPmodelFinding adistr ibutionof the gates

BenchmarkingWhy not using?

Dynamic

schedulling (w orkflow):too long to redistribute dataMaster-slave: same

Complex

algor ithm(model) = loss of confidence

BSP Execution of Homomorphic Programs12 / 26

IntroductionCingulataExecution BSPConclusion

Q: So?What can we remark?

Cingulata

gener ates boolean circuits

They are

big b utalso manipulating encr yptedbooleans

Making their execution very

slo w

Even on

m ulti-cores using par allelthreads

What can we do?

Distributed

e xecutionusing the BSPmodelFinding adistr ibutionof the gates

BenchmarkingWhy not using?

Dynamic

schedulling (w orkflow):too long to redistribute dataMaster-slave: same

Complex

algor ithm(model) = loss of confidence

BSP Execution of Homomorphic Programs12 / 26

IntroductionCingulataExecution BSPConclusion

Q: So?What can we remark?

Cingulata

gener ates boolean circuits

They are

big b utalso manipulating encr yptedbooleans

Making their execution very

slo w

Even on

m ulti-cores using par allelthreads

What can we do?

Distributed

e xecutionusing the BSPmodelFinding adistr ibutionof the gatesquotesdbs_dbs5.pdfusesText_9
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