The notion of strong designated verifier signature was put forth by Jakobsson, Sako and Impagliazzo in 1996, but the formal definition was defined recently by Saeednia, Kremer and Markowitch in 2003 and revisited by Laguil- laumie and Vergnaud in 2004. In this paper, we firstly propose the notion of short strong designated verifier sig- nature scheme, and extend it to the short identity-based strong designated verifier scheme. Then, we propose the first construction of short strong designated verifier sig- nature scheme. We also extend our scheme to construct a short identity-based strong designated verifier signature scheme. The size of the signature of our schemes is the shortest compared to any existing schemes reported in the literature. We provide formal security proofs for our schemes based on the random oracle model. Finally, we also discuss an extension of our scheme to construct a short strong designated verifier signature without random oracle.