DistributedIBE

This library implements the Threshold IBE scheme based on Boneh-Franklin scheme.

Security Parameters

This scheme relies on the hybrid encryption. We use the implementation of such scheme by FiloSottile/age which only encrypts a random symmetric key that is used to encrypt the data using Chacha20Poly1305.

The used symmetric key is of size 32 bytes. The implementation of IBE scheme used to encrypt this key uses the BLS12-381 curve.

Benchmarking Results

We have tested the efficiency of our scheme against the number of validators and message size.

The below table shows the runtime of the scheme covering share generation, key extraction, commitment verification, message encryption, key aggregation, and ciphertext decryption through different numbers of validators:

Number of Validators	Execution Time
4	10880689 ns/op
8	19333171 ns/op
16	36199305 ns/op
32	70639750 ns/op
64	144968458 ns/op
128	290355378 ns/op

Based on the above table, we can clearly see that the executrion time increases linearly with the number of validators.

Since the message is being encrypted first and the key is used for the IBE, we expect the execution time to be independent of the message size. The microbenchmarking results confirm this as shown in the below table:

Message Size (bytes)	Execution Time
8	11180636 ns/op
32	11006738 ns/op
128	11160579 ns/op
512	10927982 ns/op
2048	10927359 ns/op
8192	11029081 ns/op

We also broke down the steps to measure the overhead of each stage:

Function	Number of Validators	Execution Time
Key extraction and aggregation	128	213753903 ns/op

Function	Number of messages	Execution Time
Encryption	1	1574796 ns/op
	4	6179149 ns/op
	16	24764695 ns/op
	64	100275889 ns/op
	256	399253311 ns/op
Decryption	8	7205781 ns/op
	32	30806709 ns/op
	128	117187771 ns/op
	512	457499724 ns/op
	1024	930084488 ns/op

Message Size (bytes)	Encryption Time
8	1418055 ns/op
32	1357339 ns/op
128	1396858 ns/op
512	1385265 ns/op
2048	1410541 ns/op
8192	1356855 ns/op
32768	1406723 ns/op
131072	1412484 ns/op
524288	1385327 ns/op
1048576	1369466 ns/op
10485760	1390764 ns/op
104857600	1411491 ns/op

Number of Validators	Aggregation Time
4	4.124389 ms/op
8	8.799101 ms/op
16	16.254498 ms/op
32	32.488808 ms/op
64	63.740821 ms/op
128	129.824590 ms/op
256	263.148990 ms/op
512	548.425002 ms/op
1024	1206.202045 ms/op

Message Size (bytes)	Decryption Time
8	689101 ns/op
32	687388 ns/op
128	728981 ns/op
512	723354 ns/op
2048	698191 ns/op
8192	719345 ns/op
32768	716769 ns/op
131072	873302 ns/op

In order to improve the efficiency in case of decrypting large number of messages, we can perform the decryption in parallel. Below shows the execution times for the parallel decryption:

Function	Number of messages	Execution Time
Decryption	8	2404587 ns/op
	32	6470264 ns/op
	128	23466097 ns/op
	512	80075636 ns/op
	1024	153275583 ns/op

All benchmarks have been ran on a laptop with 12th Gen Intel(R) Core(TM) i7-1270P cpu.

KZG Commitments vs VSS

Below, we compare the verification time for KZG commitments vs VSS.

Function	Number of Validators	Execution Time
KZG Share Verification	4	4744239 ns/op
	8	9348084 ns/op
	16	18922709 ns/op
	32	38153229 ns/op
	64	77705447 ns/op
	128	154309057 ns/op
VSS Share Verification	4	383691 ns/op
	8	1521771 ns/op
	16	7168398 ns/op
	32	38691278 ns/op
	64	219296811 ns/op
	128	1039926768 ns/op
KZG Share Generation	4	641104 ns/op
	8	2612382 ns/op
	16	11231675 ns/op
	32	52606951 ns/op
	64	260647892 ns/op
	128	1075045566 ns/op
VSS Share Generation	4	191175 ns/op
	8	332393 ns/op
	16	610982 ns/op
	32	1264965 ns/op
	64	2662454 ns/op
	128	7105321 ns/op

Configuration

The following commands install the required packages and dependancies:

go mod init DistributedIBE
go mod tidy

Testing

Use the following commands to run the sample test:

cd DistributedIBE
go test

Use the below commands to run the benchmarks:

cd DistributedIBE
go test --bench=.