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Table 1.

Description of notations.

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Fig 1.

The designated-verifier scheme architecture.

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Fig 2.

Designated-verifier non-interactive zero-knowledge based on RLWE key exchange.

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Fig 2 Expand

Fig 3.

The publicly-verifiable scheme architecture.

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Fig 4.

Publicly-verifiable non-interactive zero-knowledge based on key exchange.

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Table 2.

Comparison the efficiency of related zero-knowledge proof schemes.

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Table 2 Expand

Fig 5.

Impact of the secret value size on proof size.

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Fig 5 Expand

Table 3.

Approximate comparison.

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Table 3 Expand