LUMENOS: Private Proof Delegation with FHE-SNARKs

This project aims to develop and validate Private Proof Delegation via server-side FHE-evaluated SNARKs over encrypted single-client or private shared witness and untrusted public verifiability.

Documentation

• Analysis "SNARK-FHE vs FHE-SNARK for Private Proof Delegation"
• Proposal "PPD via FHE-SNARK"

Requirements

• Linux amd64 / x86-64 system
• avx512 and aes instruction set extensions
• Go 1.23
• gcc g++ make cmake libgmp-dev libmpfr-dev unzip

Run

Build

make init-submodules build
export LD_LIBRARY_PATH=./vdec/c

Test

go test -v -run TestLigeroPPD github.com/nulltea/lumenos/fhe

Demo

Run server:

make server

Run client

make client REMOTE_SERVER_URL=http://<IP>:8080

Benchmarks

• BGV params based on GenerateBGVParamsForNTT heuristic
  • Plaintext prime: 144115188075593729 ($2^{57} – 2^{18} + 1$, $57$ bits)
  • LogN max(12, log2(ROWS)) (see table)
  • LogQ len([58, 56, 56, ... ])=log2(nttSize)
  • LogP [55,55]
• Number of queries 306 (according to ref. implementation)

Server

Dimension	2048x1024	4096x2048	8192x4096	16384x4096
LogN	12	12	13	14
Encode eval	5.17s	12.63s	1m 6.78s	2m 22.73s
Commit eval	1.03s	2.04s	9.17s	18.79s
Inner product eval	8.51s	22.74s	1m 49.60s	4m 7.48s
Query cols eval	1.10s	1.42s	3.55s	7.63s
Prove eval total	9.61s	24.17s	1m 53.16s	4m 15.12s
$ct[\langle r_i,M_{i,j}\rangle]$	135 MB	269 MB	1.1 GB	2.1 GB
$ct[\hat{M}_{i,j}] i \in \lambda$	41 MB	41 MB	81 MB	162 MB
Proof size	310 MB	579 MB	2.2 GB	4.5 GB
Peak RAM (GB)	5.74 GB	10.79 GB	41.23 GB	79.43 GB

Hardware: m7i.8xlarge, 32 vCPUs 128GB RAM

Client

Dimension	2048x1024	4096x2048	8192x4096	16384x4096
LogN	12	12	13	14
Keys	69 MB	103 MB	237 MB	504 MB
Encrypted proof size	310 MB	579 MB	2.2 GB	4.5 GB
Decrypt $ct[\hat{M}_{i,j}] i \in \lambda$	95.85ms	107.73ms	220.10ms	513.26ms
Decrypt $ct[\langle r_i,M_{i,j}\rangle]$	531.57ms	1.05s	4.32s	47.53s
Decrypt total	627.49ms	1.16s	4.54s	48.05s
Batch ciphertexts	239.94ms	261.73ms	593.67ms	1.32s
PoD prover	22.96s	22.82s	22.82s	22.70s
Public verifier	151.94ms	197.06ms	389.39ms	804.64ms
Ligero local	3.89s	16.81s	1m 20.69s	14m 21.94s
Peak RAM (GB)	1.05 GB	1.83 GB	6.34 GB	7.18 GB

Hardware: m7i.8xlarge, 2 vCPUs 8GB RAM

Experimental

• Same hardware as above.
• Server performs ring switch to LogN: 10 for inner product ciphertexts $ct[\langle r_i,M_{i,j}\rangle]$.
  • Note: correct deployment requires SlotsToCoeff ("unbatching") before ring switch which is not yet implemented for BFV. Verification is skipped because of this.
• PoD prover runs optimized GBFV version vdec_gbfv.c
  • Note: Lattigo currently does not support GBFV. So final PoD is partially invalid (h_our coeff check fails).

Server

Dimension	2048x1024	4096x2048	8192x4096	16384x4096
LogN	12	12	13	14
Encode eval	5.16s	12.72s	1m 6.39s	2m 23.12s
Commit eval	1.03s	2.04s	9.18s	18.80s
Inner product eval	8.51s	22.65s	1m 50.17s	4m 8.44s
Query cols eval	1.10s	1.41s	3.55s	7.63s
Prove eval total	9.67s	24.32s	1m 53.73s	4m 16.12s
$ct[\langle r_i,M_{i,j}\rangle]$	17 MB / -7.94x	34 MB / -7.91x	68 MB / -16.57x	68 MB / -31.62x
$ct[\hat{M}_{i,j}] i \in \lambda$	41 MB	41 MB	81 MB	162 MB
Proof size	75 MB / -4.13x	109 MB / -5.31x	218 MB / -10.33x	299 MB / -15.41x
Peak RAM (GB)	5.40 GB	10.78 GB	41.90 GB	79.25 GB

Client

Dimension	2048x1024	4096x2048	8192x4096	16384x4096
LogN	12	12	13	14
Keys	74 MB / +1.07x	110 MB / +1.07x	252 MB / +1.06x	533 MB / +1.06x
Encrypted proof size	75 MB	109 MB	218 MB	299 MB
Decrypt $ct[\hat{M}_{i,j}] i \in \lambda$	98.15ms	107.52ms	223.39ms	483.88ms
Decrypt $ct[\langle r_i,M_{i,j}\rangle]$	72.35ms / -7.35x	146.75ms / -7.15x	284.23ms / -15.19x	287.14ms / -165.52x
Decrypt total	170.58ms ~ -3.68x	254.38ms ~ -4.56x	507.71ms ~ -8.94x	771.12ms ~ -62.31x
Batch ciphertexts	243.19ms	269.33ms	595.06ms	1.26s
PoD prover	3.21s / -7.15x	3.05s / -7.48x	3.20s / -7.13x	3.20s / -7.09x
Public verifier	N/A	N/A	N/A	N/A
Ligero local	3.99s	16.66s	1m 20.11s	10m 15.22s
Peak RAM (GB)	0.56 GB / -1.88x	1.40 GB / -1.31x	5.39 GB / -1.18x	7.05 GB (≈)

Run yourself

Run the server:

./scripts/benchmark_server.sh

Run the client:

REMOTE_SERVER_URL=http://<IP>:8080 ./scripts/benchmark_client.sh

Run the client with ring switch and GBFV (experimental):

RING_SWITCH_LOGN=10 IS_GBFV=true REMOTE_SERVER_URL=http://<IP>:8080 \ 
./scripts/benchmark_client.sh -ringSwitchLogN 10