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Group signatures allow members to sign on behalf of a group while maintaining signer's identity anonymous. In this paper, we show that it is possible to reduce the public key length of the first provably secure group signature scheme from code-based assumptions without losing the security properties. More precisely, the public key can be 466 times shorter than the original scheme, typically for a group of 16 users when the public key length is 1.34 kilo-bytes, while the size is 625 kilo-bytes in the original scheme (Ezerman et al., 2015). Our technic consist in using a Quasi-cyclic Moderate Density Parity-Check McEliece variant for encrypting user identity and a random double circulant matrix for the Underlying Zero Knowledge Argument System.

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