IEEE Circuits and Systems Magazine - Q1 2021 - 40

[122] S. Salamat, M. Imani, S. Gupta, and T. Rosing, " RNSnet: In-memory
neural network acceleration using residue number system, " in Proc.
IEEE Int. Conf. Rebooting Comput. (ICRC), Nov. 2018, pp. 1-12.
[123] N. Samimi, M. Kamal, A. Afzalli-Kusha, and M. Pedram, " Res-DNN:
A residue number system-based DNN accelerator unit, " IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 67, no. 2, pp. 658-671, 2020. doi: 10.1109/
TCSI.2019.2951083.
[124] Y. Chen, T. Krishna, J. S. Emer, and V. Sze, " Eyeriss: An energyefficient reconfigurable accelerator for deep convolutional neural networks, " IEEE J. Solid-State Circuits, vol. 52, no. 1, pp. 127-138, Jan. 2017.
doi: 10.1109/JSSC.2016.2616357.
[125] Z. Torabi and G. Jaberipur, " Low-power/cost RNS comparison via
partitioning the dynamic range, " IEEE Trans. Very Large Scale Integr. (VLSI)
Syst., vol. 24, no. 5, pp. 1849-1857, May 2016. doi: 10.1109/TVLSI.2015.
2484618.
[126] M. Xu, Z. Bian, and R. Yao, " Fast sign detection algorithm for the
n+1
n
n
- 1, 2 - 1, 2 }, " IEEE Trans. Very Large Scale InRNS moduli set {2
tegr. (VLSI) Syst., vol. 23, no. 2, pp. 379-383, Feb. 2015.
[127] J. Johnson, " Rethinking floating point for deep learning, " 2018.
[Online]. Available: http://arxiv.org/abs/1811.01721
[128] U. Kulisch, Computer Arithmetic and Validity. De Gruyter, 2012.
[129] J. Gustafson and I. Yonemoto, " Beating floating point at its own
game: Posit arithmetic, " Supercomput. Frontiers Innov., Int. J., vol. 4,
no. 2, p. 71-86, June 2017.
[130] J. Yu, K. Kim, J. Lee, and K. Choi, " Accurate and efficient stochastic
computing hardware for convolutional neural networks, " in Proc. IEEE
Int. Conf. Comput. Design (ICCD), 2017, pp. 105-112.
[131] M. Alawad and M. Lin, " Stochastic-based deep convolutional
networks with reconfigurable logic fabric, " IEEE Trans. Multi-Scale
Comput. Syst., vol. 2, no. 4, pp. 242-256, 2016. doi: 10.1109/TMSCS.2016
.2601326.
[132] P. Li and D. J. Lilja, " Using stochastic computing to implement digital image processing algorithms, " in Proc. IEEE 29th Int. Conf. Comput.
Design (ICCD), 2011, pp. 154-161.
[133] A. Ren, Z. Li, C. Ding, Q. Qiu, Y. Wang, J. Li, X. Qian, and B. Yuan,
" SC-DCNN: Highly-scalable deep convolutional neural network using
stochastic computing, " in Proc. 22nd Int. Conf. Archit. Support Programming Languages Oper. Syst. (ASPLOS), 2017, pp. 405-418.
[134] A. Ardakani, F. Leduc-Primeau, N. Onizawa, T. Hanyu, and W. J.
Gross, " VLSI implementation of deep neural network using integral
stochastic computing, " IEEE Trans. Very Large Scale Integr. (VLSI)
Syst., vol. 25, no. 10, pp. 2688 -2699, 2017. doi: 10.1109/TVLSI.2017
.2654298.
[135] V. Lee, A. Alaghi, J. Hayes, V. Sathe, and L. Ceze, " Energy-efficient
hybrid stochastic-binary neural networks for near-sensor computing, "
in Proc. Conf. Design, Autom. Test Europe (DATE), 2017, pp. 13-18.
[136] H. Sim and J. Lee, " A new stochastic computing multiplier with
application to deep convolutional neural networks, " in Proc. 54th ACM/
EDAC/IEEE Design Autom. Conf. (DAC), 2017, pp. 1-6. doi: 10.1145/3061639.
3062290.
[137] R. Hojabr et al., " SkippyNN: An embedded stochastic-computing
accelerator for convolutional neural networks, " in Proc. 56th ACM/IEEE
Design Autom. Conf. (DAC), 2019, pp. 1-6.
[138] R. Rivestand, A. Shamir, and L. Adleman, " A method for obtaining digital signatures and public-key cryptosystems, " Commun. ACM,
vol. 21, no. 2, pp. 120-126, 1978. doi: 10.1145/359340.359342.
[139] P. L. Montgomery, " Modular multiplication without trial division, "
Math. Comput., vol. 44, no. 170, pp. 519-521, 1985. doi: 10.1090/S00255718-1985-0777282-X.
[140] J. Bajard, L. Didier, and P. Kornerup, " Modular multiplication and
base extensions in residue number systems, " in Proc. 15th IEEE Symp.
Comput. Arithmetic ARITH, June 2001, pp. 59-65.
[141] S. Antao, J. Bajard, and L. Sousa, " Elliptic curve point multiplication on GPUs, " in Proc. 21st IEEE Int. Conf. Appl.-specific Syst., Archit.
Process. (ASAP), 2010, pp. 192-199.
[142] L. Sousa, S. Antao, and P. Martins, " Combining residue arithmetic
to design efficient cryptographic circuits and systems, " IEEE Circuits Syst.
Mag., vol. 16, no. 4, pp. 6-32, 2016. doi: 10.1109/MCAS.2016.2614714.
[143] J. Ambrose, H. Pettenghi, and L. Sousa, " DARNS:a randomized
multi-modulo RNS architecture for double-and-add in ECC to prevent
power analysis side channel attacks, " in Proc. Asia South Pacific Design
Autom. Conf. (ASP-DAC), 2013, pp. 620-625.

40

IEEE CIRCUITS AND SYSTEMS MAGAZINE

[144] P. W. Shor, " Algorithms for quantum computation: discrete logarithms and factoring, " in Proc. 35th Annu. Symp. Found. Comput. Sci.,
Nov. 1994, pp. 124-134.
[145] NIST, 2016, p. 25. [Online]. Available: https://csrc.nist.gov/CSRC/
media/Projects/Post- Quantum- Cryptography/documents/call-for
-proposals-final-dec-2016.pdf
[146] L. Babai, " On Lovász' lattice reduction and the nearest lattice
point problem (shortened version), " in Proc. 2nd Symp. Theoretical Aspects Comput. Sci., 1985, pp. 13-20.
[147] P. Martins and L. Sousa, " The role of non-positional arithmetic
on efficient emerging cryptographic algorithms, " IEEE Access, vol. 8,
pp. 59,533-59,549, 2020. doi: 10.1109/ACCESS.2020.2983020.
[148] C. Gentry, " Fully homomorphic encryption using ideal lattices, " in
Proc. 41st Annu. ACM Symp. Theory Comput., 2009, pp. 169-178.
[149] N. Smart and F. Vercauteren, " Fully homomorphic SIMD operations, " Cryptology ePrint Archive, Rep. 2011/133, 2011.
[150] C. Gentry, S. Halevi, and N. Smart, Fully Homomorphic Encryption
with Polylog Overhead. Berlin: Springer-Verlag, 2012, pp. 465-482.
[151] P. Martins and L. Sousa, " A methodical FHE-based cloud computing model, " Future Gener. Comput. Syst., vol. 95, pp. 639-648, 2019. doi:
10.1016/j.future.2019.01.046.
[152] S. Jordan, " Quantum algorithm zoo, " 2011. [Online]. Available:
https://quantumalgorithmzoo.org/
[153] P. Shor, " Algorithms for quantum computation: discrete logarithms and factoring, " in Proc. 35th Annu. Symp. Found. Comput. Sci.,
1994, pp. 124-134.
[154] R. Jozsa, " Quantum factoring, discrete logarithms, and the hidden subgroup problem, " Comput. Sci. Eng., vol. 3, pp. 34-43, 1996. doi:
10.1109/5992.909000.
[155] P. Kaye, R. Laflamme, and M. Mosca, An Introduction to Quantum
Computing. London, U.K.: Oxford Univ. Press, 2007.
[156] D. R. Simon, " On the power of quantum computation, " in Proc. 35th
Annu. Symp. Found. Comput. Sci., 1994, pp. 116-123.
[157] R.Jozsa, " Quantum algorithms and the Fourier transform, " Proc.
Roy. Soc. London Ser. A, Math., Phys. Eng. Sci., vol. 454, no. 1969, pp. 323-
337, Jan. 1998.
[158] M. Nielsen and L. Chuang, Quantum Computation and Quantum
Information, 10th Anniversary Ed., Cambridge, U.K.: Cambridge Univ.
Press, 2011.
[159] R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, " Quantum algorithms revisited, " Proc. Roy. Soc. London Ser. A, Math., Phys. Eng. Sci.,
vol. 454, no. 1969, p. 339-354, Jan. 1998. doi: 10.1098/rspa.1998.0164.
[160] A. Asfaw et al., " Learn quantum computation using qiskit, " 2020.
[Online]. Available: http://community.qiskit.org/textbook
[161] R. Duarte, H. Neto, and M. Vestias, " Xtokaxtikox: A stochastic computing-based autonomous cyber-physical system, " in Proc.
IEEE Int. Conf. Rebooting Comput. (ICRC), 2016, pp. 1-7. doi: 10.1109/
ICRC.2016.7738716.
[162] S. Antao and L. Sousa, " The CRNS framework and its application
to programmable and reconfigurable cryptography, " ACM Trans. Archit.
Code Optimiz., vol. 9, no. 4, p. 1, 2013. doi: 10.1145/2400682.2400692.
[163] D. Boneh, C. Dunworth, R. Lipton, and J. Sgall, " On the computational power of DNA, " Discrete Appl. Math., vol. 71, no. 1, pp. 79-94, 1996.
doi: 10.1016/S0166-218X(96)00058-3.
[164] D. Lewis, " An accurate LNS arithmetic unit using interleaved memory
function interpolator, " in Proc. Symp. Comput. Arithmetic (ARITH), 1993.
[165] W. Mathworld, " Modular inverse, " [Online]. Available: https://
mathworld.wolfram.com/ModularInverse.html
[166] J. Bajard, J. Eynard, A. Hasan, and V. Zucca, " A full RNS variant of
FV like somewhat homomorphic encryption schemes, " 2016. [Online].
Available: https://eprint.iacr.org/2016/510
[167] R. Chaves and L. Sousa, " RDSP: a RISC DSP based on residue number
system, " in Proc. Euromicro Symp. Digital Syst. Design, 2003, pp. 128-135.
[168] " Quantum inspire (QI), " QuTech. [Online]. Available: https://www
.quantum-inspire.com/
[169] " Scalable quantum systems, " IBM. [Online]. Available: https://
www.ibm.com/quantum-computing/learn/what-is-ibm-q/
[170] N. Koblitz, " Elliptic curve cryptosystems, " Math. Comput., vol. 48,
no. 177, pp. 203-209, 1987. doi: 10.1090/S0025-5718-1987-0866109-5.
[171] R. Akhtar and F. A. Khanday, " Stochastic computing: Systems, applications, challenges and solutions, " in Proc. 3rd Int. Conf. Commun.
Electron. Syst. (ICCES), 2018, pp. 722-727.

FIRST QUARTER 2021
https://csrc.nist.gov/CSRC/ http://www.arxiv.org/abs/1811.01721 https://www.quantumalgorithmzoo.org/ http://community.qiskit.org/textbook https://mathworld.wolfram.com/ModularInverse.html https://mathworld.wolfram.com/ModularInverse.html https://eprint.iacr.org/2016/510 https://www.quantum-inspire.com/ https://www.quantum-inspire.com/ https://www.ibm.com/quantum-computing/learn/what-is-ibm-q/ https://www.ibm.com/quantum-computing/learn/what-is-ibm-q/
IEEE Circuits and Systems Magazine - Q1 2021

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