Handwritten　signature　verification　is　a　challenging　task　because　signatures　of　a　writer　may　be　skillfully　imitated　by　a　forger.　As　skilled　forgeries　are　generally　difficult　to　acquire　for　training,　in　this　paper,　we　propose　a　deep　learning-based　dynamic　signature　verification　framework,　SynSig2Vec,　to　address　the　skilled　forgery　attack　without　training　with　any　skilled　forgeries.　Specifically,　SynSig2Vec　consists　of　a　novel　learning-by-synthesis　method　for　training　and　a　1D　convolutional　neural　network　model,　called　Sig2Vec,　for　signature　representation　extraction.　The　learning-by-synthesis　method　first　applies　the　Sigma　Lognormal　model　to　synthesize　signatures　with　different　distortion　levels　for　genuine　template　signatures,　and　then　learns　to　rank　these　synthesized　samples　in　a　learnable　representation　space　based　on　average　precision　optimization.　The　representation　space　is　achieved　by　the　proposed　Sig2Vec　model,　which　is　designed　to　extract　fixed-length　representations　from　dynamic　signatures　of　arbitrary　lengths.　Through　this　training　method,　the　Sig2Vec　model　can　extract　extremely　effective　signature　representations　for　verification.　Our　SynSig2Vec　framework　requires　only　genuine　signatures　for　training,　yet　achieves　state-of-the-art　performance　on　the　largest　dynamic　signature　database　to　date,　DeepSignDB,　in　both　skilled　forgery　and　random　forgery　scenarios.　Source　codes　of　SynSig2Vec　will　be　available　at　https://github.com/LaiSongxuan/SynSig2Vec.　©　1979-2012　IEEE.