idash - secure genome analysis competition using oblivm€¦ · task 2a task 2b idash - secure...
TRANSCRIPT
![Page 1: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/1.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
iDASH - Secure Genome AnalysisCompetition Using ObliVM
Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan Huangand Elaine Shi
University of Maryland, College ParkIndiana University, Bloomington
![Page 2: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/2.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
ObliVM
Programming Framework for Secure
Computation
Ease-of-use: easy for non-specialist programmers to use
Efficiency: compiles programs to small circuits
![Page 3: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/3.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
ObliVM
Programming Framework for Secure
Computation
Ease-of-use: easy for non-specialist programmers to use
Efficiency: compiles programs to small circuits
![Page 4: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/4.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
ObliVM
Programming Framework for Secure
Computation
Ease-of-use: easy for non-specialist programmers to use
Efficiency: compiles programs to small circuits
![Page 5: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/5.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
![Page 6: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/6.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
ObliVM
Programming Framework for Secure
Computation
Ease-of-use: easy for non-specialist programmers to use
Efficiency: compiles programs to small circuits
Formal Security: type system is being formalized
http://oblivm.com
![Page 7: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/7.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Compute MAF
Compute minor allele frequencies
Alice Bob
CleartextSecure
AA AC AAf AliceA = 5, f AliceC = 1
AA AC CCf BobA = 3, f BobC = 3
Compute min(f AliceA + f BobA , f AliceC + f BobC )
Secure Computation: MAF = min(f AliceA + f BobA , f AliceC + f BobC )
![Page 8: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/8.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Compute MAF
Compute minor allele frequencies
Alice Bob
CleartextSecure
AA AC AAf AliceA = 5, f AliceC = 1
AA AC CCf BobA = 3, f BobC = 3
Compute min(f AliceA + f BobA , f AliceC + f BobC )
Secure Computation: MAF = min(f AliceA + f BobA , f AliceC + f BobC )
![Page 9: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/9.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Compute MAF
Compute minor allele frequencies
Alice Bob
CleartextSecure
AA AC AAf AliceA = 5, f AliceC = 1
AA AC CCf BobA = 3, f BobC = 3
Compute min(f AliceA + f BobA , f AliceC + f BobC )
Secure Computation: MAF = min(f AliceA + f BobA , f AliceC + f BobC )
![Page 10: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/10.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Code in ObliVM-lang: Compute MAF
![Page 11: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/11.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Problem Statement: Compute χ2
statistic
Task 1b: Computing χ2 statistic
AliceCase: AA AC AA
Control: AA CA CA
BobCase: AA AC CC
Control: CA AC CC
CleartextSecure
a, b: allele counts for case groupc , d : allele counts for control group(similar to Task 1A)
χ2 = n × (ad−bc)2
rsgkwhere r = a + b, s = c + d , g = a + c ,
k = b + d , n = r + s
![Page 12: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/12.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Problem Statement: Compute χ2
statistic
Task 1b: Computing χ2 statistic
AliceCase: AA AC AA
Control: AA CA CA
BobCase: AA AC CC
Control: CA AC CC
CleartextSecure
a, b: allele counts for case groupc , d : allele counts for control group(similar to Task 1A)
χ2 = n × (ad−bc)2
rsgkwhere r = a + b, s = c + d , g = a + c ,
k = b + d , n = r + s
![Page 13: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/13.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Problem Statement: Compute χ2
statistic
Task 1b: Computing χ2 statistic
AliceCase: AA AC AA
Control: AA CA CA
BobCase: AA AC CC
Control: CA AC CC
CleartextSecure
a, b: allele counts for case groupc , d : allele counts for control group(similar to Task 1A)
χ2 = n × (ad−bc)2
rsgkwhere r = a + b, s = c + d , g = a + c ,
k = b + d , n = r + s
![Page 14: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/14.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Results: Compute χ2 statistic
Floating point computation
Absolute accuracy1.11× 10−4 with 7763 gates5.6× 10−8 with 14443 gates
![Page 15: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/15.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Code in ObliVM-lang: Compute χ2
statistic
![Page 16: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/16.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Building Block: Secure Set Union
AliceSA
{a, b, c}
BobSB
{b, d, e}
Cardinality of the union of the sets i.e. |SA ∪ SB ||SA ∪ SB | = 5
CleartextSecure
Strawman solution:
O(N log2N)
union(SA,SB)
1: Sort the combined array SA||SB obliviously2: Compute cardinality in a single pass
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ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Building Block: Secure Set Union
AliceSA
{a, b, c}
BobSB
{b, d, e}
Cardinality of the union of the sets i.e. |SA ∪ SB ||SA ∪ SB | = 5
CleartextSecure
Strawman solution:
O(N log2N)
union(SA,SB)
1: Sort the combined array SA||SB obliviously2: Compute cardinality in a single pass
![Page 18: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/18.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Building Block: Secure Set Union
AliceSA
{a, b, c}
BobSB
{b, d, e}
Cardinality of the union of the sets i.e. |SA ∪ SB ||SA ∪ SB | = 5
CleartextSecure
Strawman solution:
O(N log2N)
union(SA,SB)
1: Sort the combined array SA||SB obliviously
2: Compute cardinality in a single pass
![Page 19: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/19.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Building Block: Secure Set Union
AliceSA
{a, b, c}
BobSB
{b, d, e}
Cardinality of the union of the sets i.e. |SA ∪ SB ||SA ∪ SB | = 5
CleartextSecure
Strawman solution:
O(N log2N)
union(SA,SB)
1: Sort the combined array SA||SB obliviously2: Compute cardinality in a single pass
![Page 20: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/20.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Oblivious Merge
CleartextSecure
union(SA,SB)
1: Local sort of SA and SB
2: Oblivious merge of sorted lists3: Compute cardinality in a single pass
O(N logN)
![Page 21: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/21.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Oblivious Merge
CleartextSecure
union(SA,SB)
1: Local sort of SA and SB
2: Oblivious merge of sorted lists
3: Compute cardinality in a single pass
O(N logN)
![Page 22: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/22.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Oblivious Merge
CleartextSecure
union(SA,SB)
1: Local sort of SA and SB
2: Oblivious merge of sorted lists3: Compute cardinality in a single pass
O(N logN)
![Page 23: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/23.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Code: Oblivious Merge
![Page 24: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/24.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Bloom Filter
Common case: Check for existence of elements
Our case: Approximate the cardinality of a set S
![Page 25: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/25.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Bloom Filter
Common case: Check for existence of elements
Our case: Approximate the cardinality of a set S
|S |MLE =ln(1−X
m )
k ln(1−1/m)
whereX : number of bits set,m: number of bits in the bloom filter,k : number of hash functions,|S |MLE : maximum likelihood estimate of |S |
![Page 26: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/26.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Bloom Filter
CleartextSecure
union(SA,SB)
1: Compute bloom filters locally
2: In secure computation, compute bitwise OR and count num-ber of 1’s
3: Compute estimated |S | in cleartext
O(m) operations, m: number of bits used for bloom filterm = O(N), number of elements inserted in the bloom filter
![Page 27: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/27.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Bloom Filter
CleartextSecure
union(SA,SB)
1: Compute bloom filters locally2: In secure computation, compute bitwise OR and count num-
ber of 1’s
3: Compute estimated |S | in cleartext
O(m) operations, m: number of bits used for bloom filterm = O(N), number of elements inserted in the bloom filter
![Page 28: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/28.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Bloom Filter
CleartextSecure
union(SA,SB)
1: Compute bloom filters locally2: In secure computation, compute bitwise OR and count num-
ber of 1’s3: Compute estimated |S | in cleartext
O(m) operations, m: number of bits used for bloom filterm = O(N), number of elements inserted in the bloom filter
![Page 29: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/29.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Set Union: Bloom Filter
CleartextSecure
union(SA,SB)
1: Compute bloom filters locally2: In secure computation, compute bitwise OR and count num-
ber of 1’s3: Compute estimated |S | in cleartext
O(m) operations, m: number of bits used for bloom filterm = O(N), number of elements inserted in the bloom filter
![Page 30: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/30.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Code: CountOnes
![Page 31: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/31.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Problem Statement: Hamming Distance
Alice and Bob maintain records of type (ref , svtype, alt) thatdiffer from the reference
d = 0;
for each record of type SNP or SUB
if ((x == null) || (y == null) || (x.ref ==
y.ref && x.alt != y.alt)
d += 1;
end for
![Page 32: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/32.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Solution: Hamming Distance
Alice Bob
SA ={(1, T, SNP),(75, G, SNP)} SB ={(1, T, SNP),(18, A, SNP)}
We need all positions that have been modified, but notmodified to the same value
Hamming Distance = |SA ∪ SB | − |SA ∩ SB | =|{(75,G ,SNP), (18,A, SNP)}|
![Page 33: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/33.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Problem Statement: Edit Distance
Alice and Bob maintain records of type (ref , svtype, alt) thatdiffer from the reference
Replacement: Calculate like hamming distance
Insertion/Deletion:
If one party modifies a position, add
len(alt) to edit distance
If both parties modify a position, add
len(max(alt1, alt2)) to edit distance
![Page 34: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/34.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Solution: Edit Distance
Alice{(1, T, SNP),(10, TCG, INS),(75, G, SNP)}
Bob{(1, T, SNP),(10, CA, INS),(18, A, SNP)}
SA1 = {(1, 1), (10, 1), (10, 2), (10, 3), (75, 1)}
SA2 = {(1,T , 1), (10,T , 1), (10,C , 2), (10,G , 3), (75,G , 1)}
d1 = |SA1 ∪ SB
1 | = |{(1, 1), (10, 1), (10, 2), (10, 3), (75, 1), (18, 1)}|
d2 = |SA2 ∩ SB
2 | = |{(1,T , 1)}|
Compute d1− d2
![Page 35: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/35.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Solution: Edit Distance
Alice{(1, T, SNP),(10, TCG, INS),(75, G, SNP)}
Bob{(1, T, SNP),(10, CA, INS),(18, A, SNP)}
SA1 = {(1, 1), (10, 1), (10, 2), (10, 3), (75, 1)}
SA2 = {(1,T , 1), (10,T , 1), (10,C , 2), (10,G , 3), (75,G , 1)}
d1 = |SA1 ∪ SB
1 | = |{(1, 1), (10, 1), (10, 2), (10, 3), (75, 1), (18, 1)}|
d2 = |SA2 ∩ SB
2 | = |{(1,T , 1)}|
Compute d1− d2
![Page 36: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/36.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Solution: Edit Distance
Alice{(1, T, SNP),(10, TCG, INS),(75, G, SNP)}
Bob{(1, T, SNP),(10, CA, INS),(18, A, SNP)}
SA1 = {(1, 1), (10, 1), (10, 2), (10, 3), (75, 1)}
SA2 = {(1,T , 1), (10,T , 1), (10,C , 2), (10,G , 3), (75,G , 1)}
d1 = |SA1 ∪ SB
1 | = |{(1, 1), (10, 1), (10, 2), (10, 3), (75, 1), (18, 1)}|
d2 = |SA2 ∩ SB
2 | = |{(1,T , 1)}|
Compute d1− d2
![Page 37: iDASH - Secure Genome Analysis Competition Using ObliVM€¦ · Task 2A Task 2B iDASH - Secure Genome Analysis Competition Using ObliVM Xiao Shaun Wang, Chang Liu, Kartik Nayak, Yan](https://reader036.vdocuments.mx/reader036/viewer/2022071113/5fea9070ad511627013dc632/html5/thumbnails/37.jpg)
ObliVM
Task 1A
Task 1B
Set union
Task 2A
Task 2B
Solution: Edit Distance
Alice{(1, T, SNP),(10, TCG, INS),(75, G, SNP)}
Bob{(1, T, SNP),(10, CA, INS),(18, A, SNP)}
SA1 = {(1, 1), (10, 1), (10, 2), (10, 3), (75, 1)}
SA2 = {(1,T , 1), (10,T , 1), (10,C , 2), (10,G , 3), (75,G , 1)}
d1 = |SA1 ∪ SB
1 | = |{(1, 1), (10, 1), (10, 2), (10, 3), (75, 1), (18, 1)}|
d2 = |SA2 ∩ SB
2 | = |{(1,T , 1)}|
Compute d1− d2