Certificateless network coding proxy signatures from lattice

doi:10.1007/s11704-022-2128-z

Front. Comput. Sci.

2023, Vol. 17

Issue (5) : 175810 https://doi.org/10.1007/s11704-022-2128-z

RESEARCH ARTICLE

Certificateless network coding proxy signatures from lattice

Huifang YU(

), Ning WANG

School of Cyberspace Security, Xi’an University of Posts & Telecommunications, Xi’an 710121, China

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Abstract

Network coding can improve the information transmission efficiency and reduces the network resource consumption, so it is a very good platform for information transmission. Certificateless proxy signatures are widely applied in information security fields. However, certificateless proxy signatures based on classical number theory are not suitable for the network coding environment and cannot resist the quantum computing attacks. In view of this, we construct certificateless network coding proxy signatures from lattice (LCL-NCPS). LCL-NCPS is new multi-source signature scheme which has the characteristics of anti-quantum, anti-pollution and anti-forgery. In LCL-NCPS, each source node user can output a message vector to intermediate node and sink node, and the message vectors from different source nodes will be linearly combined to achieve the aim of improving the network transmission rate and network robustness. In terms of efficiency analysis of space dimension, LCL-NCPS can obtain the lower computation complexity by reducing the dimension of proxy key. In terms of efficiency analysis of time dimension, LCL-NCPS has higher computation efficiency in signature and verification.

Keywords lattice multi-source signature scheme proxy signature post-quantum

Corresponding Author(s): Huifang YU

Just Accepted Date: 07 September 2022 Issue Date: 12 December 2022

Cite this article:

Huifang YU,Ning WANG. Certificateless network coding proxy signatures from lattice[J]. Front. Comput. Sci., 2023, 17(5): 175810.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-022-2128-z
https://academic.hep.com.cn/fcs/EN/Y2023/V17/I5/175810

Fig.1 Multi-source transmission network model

Fig.2 Flowchart about proxy signature and combination

Feature comparison	Literature [26]	Literature [27]	Literature [28]	LCL-NCPS
Anti-quantum attacks	No	No	No	Yes
Anti-pollution attacks	Yes	Yes	Yes	Yes
Key escrow	Yes	No	No	No
Unforgeability	Yes	Yes	Yes	Yes
Signature length	$O (l 2 n ? 1 n l b (n))$	$O (2 m + n n 2 l b (n))$	$O (2 n ? 1 n l b (n))$	$O (m l b (12 σ))$

Tab.1 Feature comparison of several schemes

Various cryptography operation	Symbols
Time to execute an elliptic curve point multiplication operation	$C e c p$
Time to execute a scalar multiplication	$C m u l$
Time to execute a hash operation	$C m t p$
Time to execute an exponential operation	$C m e$
Time to execute a bilinear operation	$C p a r$
Time to execute image sampling algorithm	$S T$
Time to execute Gaussian sampling algorithm	$S D$
Time to execute matrix vector multiplication	$M v$

Tab.2 Symbolic representation of various cryptographic operations

Symbols	Operation time/ms
$C e c p$	7.67
$C m u l$	0.02
$C m t p$	19.4
$C m e$	7.4
$C p a r$	25.38
$S T$	35.42
$S D$	23.03
$M v$	5.32

Tab.3 Operation time of various cryptographic operations

Schemes	Signature time	Verification time
Literature [26]	$2 n C m u l + (2 n + 2) C m e$	$(m + n) C m u l + (m + n + 1) C m e + C p a r$
Literature [27]	$(m + 2) C m u l + m C m e + n C e c p + 2 C m t p$	$(2 m ? 2) C m u l + (n + 2) C e c p + 2 C m t p$
Literature [28]	$(m + n) C m u l + (m + n + 1) C m e + C m t p$	$(m + n) C m u l + 2 m C p a r + C m t p$
LCL-NCPS	$(m + 2) M v + m S D + 3 C m t p + S T$	$(2 m + 3) M v + m S D + 3 C m t p + m C m u l$

Tab.4 Efficiency comparison between LCL-NCPS and similar schemes

Fig.3 Signature time comparison

Fig.4 Signature time comparison verification time comparison

$m$	$n$	$m + n$
20	180	200
30	270	300
40	360	400
50	450	500
60	540	600

Tab.5 Change of

m + n

of message vector network coding

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