High-Speed Fully Homomorphic Encryption Over the Integers

A fully homomorphic encryption (FHE) scheme is envisioned as a key cryptographic tool in building a secure and reliable cloud computing environment, as it allows arbitrary evaluation of a ciphertext without revealing the plaintext. However, existing FHE implementations remain impractical due to very high time and resource costs. To the authors’ knowledge, this paper presents the first hardware implementation of a full encryption primitive for FHE over the integers using FPGA technology. A large-integer multiplier architecture utilising Integer-FFT multiplication is proposed, and a large-integer Barrett modular reduction module is designed incorporating the proposed multiplier. The encryption primitive used in the integer-based FHE scheme is designed employing the proposed multiplier and modular reduction modules. The designs are verified using the Xilinx Virtex-7 FPGA platform. Experimental results show that a speed improvement factor of up to 44 is achievable for the hardware implementation of the FHE encryption scheme when compared to its corresponding software implementation. Moreover, performance analysis shows further speed improvements of the integer-based FHE encryption primitives may still be possible, for example through further optimisations or by targeting an ASIC platform.

Marine or estuarine radiocarbon reservoir corrections for mollusks? A case study from a medieval site in the south of England

Mollusk shells are frequently radiocarbon dated and provide reliable calibrated age ranges when the regional marine reservoir correction is well-established. For mollusks from an estuarine environment the reservoir correction may be significantly different than the regional marine reservoir correction due to the input of bedrock or soil derived carbonates. Some mollusk species such as oysters are tolerant of a significant range of salinities which makes it difficult to determine which reservoir correction is appropriate. A case study is presented of an anomalous radiocarbon age for an oyster shell paint dish found in the fabric of the ruined nave walls of St Mary's Church, Shoreham-by-Sea, West Sussex, England. Stable isotopes (delta O-18 and delta C-13) were used to establish the type of environment in which the oyster had lived. Paired marine and terrestrial samples from a nearby medieval site were radiocarbon dated to provide an appropriate reservoir correction.