• 例︓FFT/NTTで使⽤する「ひねり係数」 • リソース消費量の削減 • FFT/NTTではなく、Karatsuba法を活⽤(Miglioreら[15]) →レイテンシ…1.2倍(NTT⽐),リソース消費量…半分(NTT⽐) • FFT/NTTで使⽤する「ひねり係数」をon-the-flyで計算(Royら[14]) [14] S. Sinha Roy, K. J¨arvinen, J. Vliegen, F. Vercauteren, and I. Verbauwhede. Hepcloud: An fpga-based multicore processor for fv somewhat homomorphic function evaluation. IEEE Transactions on Computers, Vol. 67, No. 11, pp. 1637–1650, 2018. [15] V. Migliore, M. M. Real, V. Lapotre, A. Tisserand, C. Fontaine, and G. Gogniat. Hardware/software co-design of an accelerator for fv homomorphic encryption scheme using Karatsuba algorithm. IEEE Transactions on Computers, Vol. 67, No. 3, pp. 335–347, 2018. [16] A. C. Mert, E. O¨ ztu¨rk, and E. Savas¸. Design and implementation of encryption/decryption architectures for bfv homomorphic encryption scheme. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, Vol. 28, No. 2, pp. 353–362, 2020. 23 4. 実⽤上の課題に対する既存⼿法 回路の規模を ⼩さくする
→リソース消費量…半分(NTT⽐) [15] V. Migliore, M. M. Real, V. Lapotre, A. Tisserand, C. Fontaine, and G. Gogniat. Hardware/software co-design of an accelerator for fv homomorphic encryption scheme using Karatsuba algorithm. IEEE Transactions on Computers, Vol. 67, No. 3, pp. 335–347, 2018. 24 4. 実⽤上の課題に対する既存⼿法
273.6倍の⾼速化(CPU⽐) • CRTに加え、NTTを適⽤(Lupascuら[10]) データ表現に⽤いられる多項式の次数が⼩さいと、恩恵が少ないと報告している。 [10] C. Lupascu, M. Togan, and V. Patriciu. Acceleration techniques for fully-homomorphic encryption schemes. In 2019 22nd International Conference on Control Systems and Computer Science (CSCS), pp. 118–122, 2019. [28] W. Wang, Z. Chen, and X. Huang. Accelerating leveled fully homomorphic encryption using gpu. In 2014 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2800–2803, 2014. 25 4. 実⽤上の課題に対する既存⼿法
(Lupascuら[10]) [10] C. Lupascu, M. Togan, and V. Patriciu. Acceleration techniques for fully-homomorphic encryption schemes. In 2019 22nd International Conference on Control Systems and Computer Science (CSCS), pp. 118–122, 2019. 26 4. 実⽤上の課題に対する既存⼿法
techniques for fully-homomorphic encryption schemes. In 2019 22nd International Conference on Control Systems and Computer Science (CSCS), pp. 118–122, 2019. [28] W. Wang, Z. Chen, and X. Huang. Accelerating leveled fully homomorphic encryption using gpu. In 2014 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2800–2803, 2014. [14] S. Sinha Roy, K. J¨arvinen, J. Vliegen, F. Vercauteren, and I. Verbauwhede. Hepcloud: An fpga-based multicore processor for fv somewhat homomorphic function evaluation. IEEE Transactions on Computers, Vol. 67, No. 11, pp. 1637–1650, 2018. [15] V. Migliore, M. M. Real, V. Lapotre, A. Tisserand, C. Fontaine, and G. Gogniat. Hardware/software co-design of an accelerator for fv homomorphic encryption scheme using Karatsuba algorithm. IEEE Transactions on Computers, Vol. 67, No. 3, pp. 335–347, 2018. [16] A. C. Mert, E. O¨ ztu¨rk, and E. Savas¸. Design and implementation of encryption/decryption architectures for bfv homomorphic encryption scheme. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, Vol. 28, No. 2, pp. 353–362, 2020. [29] J.A. Buchmann. Einfüehrung in die Kryptographie, Springer-Verlag, Berlin Heidelberg(2003). 林芳樹(訳) 暗号理論⼊⾨ 原書第3版, 丸善出版(2012). [30] J.W. Cooley and J.W. Tukey, An Algorithm for the Machine Calculation of Complex Fourier Series, Mathematics of Computation, vol.19, pp.297–301, 1965. [31] Karatsuba, Anatolii Alexeevich. The complexity of computations. Proceedings of the Steklov Institute of Mathematics-Interperiodics Translation, 211, pp. 169– 183, 1995. 38