TY - UNPB

T1 - Verifiable Computing Using Computation Fingerprints Within FHE

AU - Dolev, Shlomi

AU - Kalma, Arseni

PY - 2021/5/1

Y1 - 2021/5/1

N2 - We suggest using Fully Homomorphic Encryption (FHE) to be used, not only
to keep the privacy of information but also, to verify computations with
no additional significant overhead, using only part of the variables
length for verification. This method supports the addition of encrypted
values as well as multiplication of encrypted values by the addition of
their logarithmic representations and is based on a separation between
hardware functionalities. The computer/server performs blackbox
additions and is based on the separation of server/device/hardware, such
as the enclave, that may deal with additions of logarithmic values and
exponentiation. The main idea is to restrict the computer operations and
to use part of the variable for computation verification (computation
fingerprints) and the other for the actual calculation. The verification
part holds the FHE value, of which the calculated result is known
(either due to computing locally once or from previous verified
computations) and will be checked against the returned FHE value. We
prove that a server with bit computation granularity can return
consistent encrypted wrong results even when the public key is not
provided. For the case of computer word granularity the verification and
the actual calculation parts are separated, the verification part (the
consecutive bits from the LSB to the MSB of the variables) is fixed
across all input vectors. We also consider the case of Single
Instruction Multiple Data (SIMD) where the computation fingerprints
index in the input vectors is fixed across all vectors.

AB - We suggest using Fully Homomorphic Encryption (FHE) to be used, not only
to keep the privacy of information but also, to verify computations with
no additional significant overhead, using only part of the variables
length for verification. This method supports the addition of encrypted
values as well as multiplication of encrypted values by the addition of
their logarithmic representations and is based on a separation between
hardware functionalities. The computer/server performs blackbox
additions and is based on the separation of server/device/hardware, such
as the enclave, that may deal with additions of logarithmic values and
exponentiation. The main idea is to restrict the computer operations and
to use part of the variable for computation verification (computation
fingerprints) and the other for the actual calculation. The verification
part holds the FHE value, of which the calculated result is known
(either due to computing locally once or from previous verified
computations) and will be checked against the returned FHE value. We
prove that a server with bit computation granularity can return
consistent encrypted wrong results even when the public key is not
provided. For the case of computer word granularity the verification and
the actual calculation parts are separated, the verification part (the
consecutive bits from the LSB to the MSB of the variables) is fixed
across all input vectors. We also consider the case of Single
Instruction Multiple Data (SIMD) where the computation fingerprints
index in the input vectors is fixed across all vectors.

KW - Computer Science - Cryptography and Security

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T3 - arxiv cs.DC

BT - Verifiable Computing Using Computation Fingerprints Within FHE

ER -