Faster matrix approximate homomorphic encryption

Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Hu, Jifa [verfasserIn] Wang, Fuqun [verfasserIn] Chen, Kefei [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Approximate homomorphic encryption Fully homomorphic encryption Matrix multiplication Half-cut transformation

Übergeordnetes Werk:	Enthalten in: Computer standards & interfaces - Amsterdam : Elsevier Science Publ. BV (North-Holland), 1986, 87
Übergeordnetes Werk:	volume:87

DOI / URN:	10.1016/j.csi.2023.103775

Katalog-ID:	ELV062439057

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520			\|a Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme.
650		4	\|a Approximate homomorphic encryption
650		4	\|a Fully homomorphic encryption
650		4	\|a Matrix multiplication
650		4	\|a Half-cut transformation
700	1		\|a Wang, Fuqun \|e verfasserin \|0 (orcid)0000-0002-6178-3630 \|4 aut
700	1		\|a Chen, Kefei \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Computer standards & interfaces \|d Amsterdam : Elsevier Science Publ. BV (North-Holland), 1986 \|g 87 \|h Online-Ressource \|w (DE-627)265782694 \|w (DE-600)1466180-9 \|w (DE-576)074890670 \|x 0920-5489 \|7 nnns
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Indexfelder

author_variant	j h jh f w fw k c kc
matchkey_str	article:09205489:2023----::atrarxprxmthmmrh
hierarchy_sort_str	2023
bklnumber	54.21
publishDate	2023
allfields	10.1016/j.csi.2023.103775 doi (DE-627)ELV062439057 (ELSEVIER)S0920-5489(23)00056-9 DE-627 ger DE-627 rda eng 004 VZ 54.21 bkl Hu, Jifa verfasserin (orcid)0000-0003-0658-9875 aut Faster matrix approximate homomorphic encryption 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme. Approximate homomorphic encryption Fully homomorphic encryption Matrix multiplication Half-cut transformation Wang, Fuqun verfasserin (orcid)0000-0002-6178-3630 aut Chen, Kefei verfasserin aut Enthalten in Computer standards & interfaces Amsterdam : Elsevier Science Publ. BV (North-Holland), 1986 87 Online-Ressource (DE-627)265782694 (DE-600)1466180-9 (DE-576)074890670 0920-5489 nnns volume:87 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.21 Rechnerperipherie Datenkommunikationshardware VZ AR 87
spelling	10.1016/j.csi.2023.103775 doi (DE-627)ELV062439057 (ELSEVIER)S0920-5489(23)00056-9 DE-627 ger DE-627 rda eng 004 VZ 54.21 bkl Hu, Jifa verfasserin (orcid)0000-0003-0658-9875 aut Faster matrix approximate homomorphic encryption 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme. Approximate homomorphic encryption Fully homomorphic encryption Matrix multiplication Half-cut transformation Wang, Fuqun verfasserin (orcid)0000-0002-6178-3630 aut Chen, Kefei verfasserin aut Enthalten in Computer standards & interfaces Amsterdam : Elsevier Science Publ. BV (North-Holland), 1986 87 Online-Ressource (DE-627)265782694 (DE-600)1466180-9 (DE-576)074890670 0920-5489 nnns volume:87 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.21 Rechnerperipherie Datenkommunikationshardware VZ AR 87
allfields_unstemmed	10.1016/j.csi.2023.103775 doi (DE-627)ELV062439057 (ELSEVIER)S0920-5489(23)00056-9 DE-627 ger DE-627 rda eng 004 VZ 54.21 bkl Hu, Jifa verfasserin (orcid)0000-0003-0658-9875 aut Faster matrix approximate homomorphic encryption 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme. Approximate homomorphic encryption Fully homomorphic encryption Matrix multiplication Half-cut transformation Wang, Fuqun verfasserin (orcid)0000-0002-6178-3630 aut Chen, Kefei verfasserin aut Enthalten in Computer standards & interfaces Amsterdam : Elsevier Science Publ. BV (North-Holland), 1986 87 Online-Ressource (DE-627)265782694 (DE-600)1466180-9 (DE-576)074890670 0920-5489 nnns volume:87 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.21 Rechnerperipherie Datenkommunikationshardware VZ AR 87
allfieldsGer	10.1016/j.csi.2023.103775 doi (DE-627)ELV062439057 (ELSEVIER)S0920-5489(23)00056-9 DE-627 ger DE-627 rda eng 004 VZ 54.21 bkl Hu, Jifa verfasserin (orcid)0000-0003-0658-9875 aut Faster matrix approximate homomorphic encryption 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme. Approximate homomorphic encryption Fully homomorphic encryption Matrix multiplication Half-cut transformation Wang, Fuqun verfasserin (orcid)0000-0002-6178-3630 aut Chen, Kefei verfasserin aut Enthalten in Computer standards & interfaces Amsterdam : Elsevier Science Publ. BV (North-Holland), 1986 87 Online-Ressource (DE-627)265782694 (DE-600)1466180-9 (DE-576)074890670 0920-5489 nnns volume:87 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.21 Rechnerperipherie Datenkommunikationshardware VZ AR 87
allfieldsSound	10.1016/j.csi.2023.103775 doi (DE-627)ELV062439057 (ELSEVIER)S0920-5489(23)00056-9 DE-627 ger DE-627 rda eng 004 VZ 54.21 bkl Hu, Jifa verfasserin (orcid)0000-0003-0658-9875 aut Faster matrix approximate homomorphic encryption 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme. Approximate homomorphic encryption Fully homomorphic encryption Matrix multiplication Half-cut transformation Wang, Fuqun verfasserin (orcid)0000-0002-6178-3630 aut Chen, Kefei verfasserin aut Enthalten in Computer standards & interfaces Amsterdam : Elsevier Science Publ. BV (North-Holland), 1986 87 Online-Ressource (DE-627)265782694 (DE-600)1466180-9 (DE-576)074890670 0920-5489 nnns volume:87 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.21 Rechnerperipherie Datenkommunikationshardware VZ AR 87
language	English
source	Enthalten in Computer standards & interfaces 87 volume:87
sourceStr	Enthalten in Computer standards & interfaces 87 volume:87
format_phy_str_mv	Article
bklname	Rechnerperipherie Datenkommunikationshardware
institution	findex.gbv.de
topic_facet	Approximate homomorphic encryption Fully homomorphic encryption Matrix multiplication Half-cut transformation
dewey-raw	004
isfreeaccess_bool	false
container_title	Computer standards & interfaces
authorswithroles_txt_mv	Hu, Jifa @@aut@@ Wang, Fuqun @@aut@@ Chen, Kefei @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	265782694
dewey-sort	14
id	ELV062439057
language_de	englisch
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title	Faster matrix approximate homomorphic encryption
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title_sort	faster matrix approximate homomorphic encryption
title_auth	Faster matrix approximate homomorphic encryption
abstract	Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme.
abstractGer	Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme.
abstract_unstemmed	Approximate Homomorphic Encryption (AHE) becomes a research hot spot in homomorphic cryptography in recent years as it is widely used in neural network, deep learning and so on. Since matrix multiplication is frequently used in these applications, many researcher have studied on it. In this paper, we propose a new matrix approximate homomorphic encryption scheme with faster matrix homomorphic multiplication. To this end, we homomorphically simulate the Strassen’s algorithm based on CKKS scheme to achieve the faster matrix approximate homomorphic multiplication, which reduces the complexity of the matrix homomorphic multiplication from O ( N 3 ) to C m i n N log 7 , where C m i n is a positive constant. The simulation is realized by the half-cut transformation of the encoded polynomials. Additionally, we estimate the upper bound of the noise for the correctness of the scheme.
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title_short	Faster matrix approximate homomorphic encryption
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