arXiv subjects

Sajjad Akherati

Publications and source records attributed to Sajjad Akherati.

5 recordsLinked to original sources

arXiv2026

Triple-Hoisted Baby-Step Giant-Step Linear Transformation over CKKS Homomorphic Encryption and Hardware Accelerator

Computations can be directly carried out over ciphertexts using homomorphic encryption (HE), which is indispensable for privacy-preserving cloud computing. Linear transformation is widely used in neural networks, including large language models. However, the implementation of linear transformation over HE requires a large number of ciphertext rotations, which incur significant memory and hardware overhead despite existing simplification techniques. This paper proposes a triple-hoisted baby-step giant-step algorithm that decomposes the baby step further to substantially reduce the number of ciphertext rotations needed for the CKKS HE evaluation of linear transformation. Moreover, to reduce off-chip memory access, which contributes to the majority of the latency, a memory-optimized data path is proposed by partitioning the algorithm into multiple phases. Furthermore, an efficient FPGA-based hardware accelerator with an optimized permutation circuit for message routing is designed for the proposed scheme. For a set of typical parameters, the proposed design reduces the off-chip memory access by 2.9x compared to the best prior design. Synthesized for Xilinx Virtex UltraScale+ devices, the proposed design achieves a 5.8x reduction in computational latency compared with the baseline design.

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arXiv2026

Multi-Input Ciphertext Multiplication for Homomorphic Encryption

Homomorphic encryption (HE) enables arithmetic operations to be performed directly on encrypted data. It is essential for privacy-preserving applications such as machine learning, medical diagnosis, and financial data analysis. In popular HE schemes, ciphertext multiplication is only defined for two inputs. However, the multiplication of multiple inputs is needed in many HE applications. In our previous work, a three-input ciphertext multiplication method for the CKKS HE scheme was developed. This paper first reformulates the three-input ciphertext multiplication to enable the combination of computations in order to further reduce the complexity. The second contribution is extending the multiplication to multiple inputs without compromising the noise overhead. Additional evaluation keys are introduced to achieve relinearization of polynomial multiplication results. To minimize the complexity of the large number of rescaling units in the multiplier, a theoretical analysis is developed to relocate the rescaling, and a multi-level rescaling approach is proposed to implement combined rescaling with complexity similar to that of a single rescaling unit. Guidelines and examples are provided on the input partition to enable the combination of more rescaling. Additionally, efficient hardware architectures are designed to implement our proposed multipliers. The improved three-input ciphertext multiplier reduces the logic area and latency by 15% and 50%, respectively, compared to the best prior design. For multipliers with more inputs, ranging from 4 to 12, the architectural analysis reveals 32% savings in area and 45% shorter latency, on average, compared to prior work.

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arXiv2025

Efficient Homomorphically Encrypted Convolutional Neural Network Without Rotation

Privacy-preserving neural network (NN) inference can be achieved by utilizing homomorphic encryption (HE), which allows computations to be directly carried out over ciphertexts. Popular HE schemes are built over large polynomial rings. To allow simultaneous multiplications in the convolutional (Conv) and fully-connected (FC) layers, multiple input data are mapped to coefficients in the same polynomial, so are the weights of NNs. However, ciphertext rotations are necessary to compute the sums of products and/or incorporate the outputs of different channels into the same polynomials. Ciphertext rotations have much higher complexity than ciphertext multiplications and contribute to the majority of the latency of HE-evaluated Conv and FC layers. This paper proposes a novel reformulated server-client joint computation procedure and a new filter coefficient packing scheme to eliminate ciphertext rotations without affecting the security of the HE scheme. Our proposed scheme also leads to substantial reductions on the number of coefficient multiplications needed and the communication cost between the server and client. For various plain-20 classifiers over the CIFAR-10/100 datasets, our design reduces the running time of the Conv and FC layers by 15.5% and the communication cost between client and server by more than 50%, compared to the best prior design.

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arXiv2024

Three-Input Ciphertext Multiplication for Homomorphic Encryption

Homomorphic encryption (HE) allows computations to be directly carried out on ciphertexts and is essential to privacy-preserving computing, such as neural network inference, medical diagnosis, and financial data analysis. Only addition and 2-input multiplication are defined over ciphertexts in popular HE schemes. However, many HE applications involve non-linear functions and they need to be approximated using high-order polynomials to maintain precision. To reduce the complexity of these computations, this paper proposes 3-input ciphertext multiplication. One extra evaluation key is introduced to carry out the relinearization step of ciphertext multiplication, and new formulas are proposed to combine computations and share intermediate results. Compared to using two consecutive 2- input multiplications, computing the product of three ciphertexts utilizing the proposed scheme leads to almost a half of the latency, 29% smaller silicon area, and lower noise without scarifying the throughput.

cs.CR↗

arXiv2024

Low-Complexity Integer Divider Architecture for Homomorphic Encryption

Homomorphic encryption (HE) allows computations to be directly carried out on ciphertexts and enables privacy-preserving cloud computing. The computations on the coefficients of the polynomials involved in HE are always followed by modular reduction, and the overall complexity of ciphertext multiplication can be reduced by utilizing the quotient. Our previous design considers the cases that the dividend is an integer multiple of the modulus and the modulus is in the format of $2^w-2^u\pm1$, where $u<w/2$. In this paper, the division is generalized for larger $u$ and dividend not an integer multiple of the modulus. An algorithm is proposed to compute the quotient and vigorous mathematical proofs are provided. Moreover, efficient hardware architecture is developed for implementing the proposed algorithm. Compared to alternative division approaches that utilize the inverse of the divisor, for $w=32$, the proposed design achieves at least 9% shorter latency and 79\% area reduction for 75% possible values of $u$.

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