A Verifiable Multi-recipient Encryption Scheme from Multilinear Maps

Jing, Zhengjun; Jiang, Guoping; Gu, Chunsheng

doi:10.1109/3pgcic.2014.49

Cited by 1 publication

(2 citation statements)

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“…Recently, multilinear map has received much attention from cryptographic researchers, and as an extended tool of bilinear pairing, multiple linear pairs have also been applied successfully. For example, Coron described a cryptanalysis of the GGH15 multilinear maps, which breaks the multipartite key‐agreement protocol by generating an equivalent user private key; in 2013, Coron et al constructed a practical multilinear map over the integers instead of ideal lattice to prove the complete randomization of encoding values for the first time; Zheng et al proposed a verifiable multi‐recipient encryption scheme from multilinear map, which has semantic security against chosen plaintext attack. Hence, it is a breakthrough to construct a common cryptographic schemes by using multilinear maps.…”

Section: Related Workmentioning

confidence: 99%

“…Multilinear discrete logarithm problem: Let G be a finite cyclic group with prime order q , for all k > 1,1⩽ i ⩽ k and g i ∈ G , given ( i , g i , a g i ) for some

a \in Z_{q}^{*}

, it is difficult to compute a . n‐Multilinear computational Diffie–Hellman problem : Given g , a 1 g , a 2 g ,…, a n g ∈ G 1 for some random choices

a_{1}, a_{2}, \dots, a_{n} \in Z_{q}^{*}

, where g is a generator of group G 1 , it is hard to compute

e_{n} {(g, g, \dots, g)}^{a_{1} a_{2} \dots a_{n}} \in G_{2}

.An algorithm is said to have advantage ϵ in solving the MDH in ( G 1 , G 2 , e ).If

\Pr [A (g, a_{1} g, a_{2} g, \dots, a_{n} g) = e_{n} {(g, \dots, g)}^{a_{1} a_{2} \dots a_{n}}] ⩾ ϵ

.Here, the probability is measured over the random choices of

a_{1}, a_{2}, \dots, a_{n} \in Z_{q}^{*}, g \in G_{1}

. MDH assumption: No probabilistic polynomial time algorithm has non‐negligible advantage ϵ in solving the MDH problem for ( G 1 , G 2 , e ).…”

Section: Preliminariesmentioning

confidence: 99%

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Publicly verifiable secret sharing scheme and its application with almost optimal information rate

Peng

Tian

2016

Security Comm Networks

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It is well known that the construction of publicly verifiable secret sharing scheme with high information rate is a challenge. The information rates of the existing schemes are generally less than one‐half; for this problem, we put forward a publicly verifiable secret sharing scheme with almost optimal information rate based on multilinear Diffie–Hellman assumption. First, we construct a knowledge commitment scheme by using multilinear map; on the basis of this scheme, we propose a publicly verifiable secret sharing scheme whose information rate is (m − 1)/m (The secret is (m − 1)‐dimensional vector), which is almost asymptotically optimal. Second, the public verifiability of the scheme is achieved by using the multiple linear property of a multilinear map. Again, under multilinear Diffie–Hellman assumption, we proved the security of our scheme. And we apply our publicly verifiable secret sharing scheme to public‐key encryption system skillfully. At last, the performance analysis results show the effectiveness and practicality of our scheme. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: Related Workmentioning

confidence: 99%

“…Multilinear discrete logarithm problem: Let G be a finite cyclic group with prime order q , for all k > 1,1⩽ i ⩽ k and g i ∈ G , given ( i , g i , a g i ) for some

a \in Z_{q}^{*}

, it is difficult to compute a . n‐Multilinear computational Diffie–Hellman problem : Given g , a 1 g , a 2 g ,…, a n g ∈ G 1 for some random choices

a_{1}, a_{2}, \dots, a_{n} \in Z_{q}^{*}

, where g is a generator of group G 1 , it is hard to compute

e_{n} {(g, g, \dots, g)}^{a_{1} a_{2} \dots a_{n}} \in G_{2}

.An algorithm is said to have advantage ϵ in solving the MDH in ( G 1 , G 2 , e ).If

\Pr [A (g, a_{1} g, a_{2} g, \dots, a_{n} g) = e_{n} {(g, \dots, g)}^{a_{1} a_{2} \dots a_{n}}] ⩾ ϵ

.Here, the probability is measured over the random choices of

a_{1}, a_{2}, \dots, a_{n} \in Z_{q}^{*}, g \in G_{1}

. MDH assumption: No probabilistic polynomial time algorithm has non‐negligible advantage ϵ in solving the MDH problem for ( G 1 , G 2 , e ).…”

Section: Preliminariesmentioning

confidence: 99%

Publicly verifiable secret sharing scheme and its application with almost optimal information rate

Peng

Tian

2016

Security Comm Networks

View full text Add to dashboard Cite

show abstract

A Verifiable Multi-recipient Encryption Scheme from Multilinear Maps

Cited by 1 publication

References 18 publications

Publicly verifiable secret sharing scheme and its application with almost optimal information rate

Publicly verifiable secret sharing scheme and its application with almost optimal information rate

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