We present here a systematic search for cyanopolyynes in the shock region L1157-B1 and its associated protostar L1157-mm in the framework of the Large Program Astrochemical Surveys At IRAM (ASAI), dedicated to chemical surveys of solar-type star forming regions with the IRAM 30m telescope. Observations of the millimeter windows between 72 and 272 GHz permitted the detection of HC$_3$N and its $^{13}$C isotopologues, and HC$_5$N (for the first time in a protostellar shock region). In the shock, analysis of the line profiles shows that the emission arises from the outflow cavities associated with L1157-B1 and L1157-B2. Molecular abundances and excitation conditions were obtained from analysis of the Spectral Line Energy Distributions under the assumption of Local Thermodynamical Equilibrium or using a radiative transfer code in the Large Velocity Gradient approximation. Towards L1157mm, the HC$_3$N emission arises from the cold envelope ($T_{rot}=10$ K) and a higher-excitation region ($T_{rot}$= $31$ K) of smaller extent around the protostar. We did not find any evidence of $^{13}$C or D fractionation enrichment towards L1157-B1. We obtain a relative abundance ratio HC$_3$N/HC$_5$N of 3.3 in the shocked gas. We find an increase by a factor of 30 of the HC$_3$N abundance between the envelope of L1157-mm and the shock region itself. Altogether, these results are consistent with a scenario in which the bulk of HC$_3$N was produced by means of gas phase reactions in the passage of the shock. This scenario is supported by the predictions of a parametric shock code coupled with the chemical model UCL_CHEM.
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