We define a (symmetric key) encryption of a signal s ∈ R N as a random mapping s → y = (y 1 , . . . , y M ) T ∈ R M known both to the sender and a recipient. In general the recipients may have access only to images y corrupted by an additive noise. Given the Encryption Redundancy Parameter (ERP) µ = M/N ≥ 1, the signal strength parameter R = i s 2 i /N , and the ('bare') noise-to-signal ratio (NSR) γ ≥ 0, we consider the problem of reconstructing s from its corrupted image by a Least Square Scheme for a certain class of random Gaussian mappings. The problem is equivalent to finding the configuration of minimal energy in a certain version of spherical spin glass model, with squared Gaussian random interaction potential. We use the Parisi replica symmetry breaking scheme to evaluate the mean overlap p ∞ ∈ [0, 1] between the original signal and its recovered image (known as 'estimator') as N → ∞, which is a measure of the quality of the signal reconstruction. We explicitly analyze the general case of linear-quadratic family of random mappings and discuss the full p ∞ (γ) curve. When nonlinearity exceeds a certain threshold but redundancy is not yet too big, the replica symmetric solution is necessarily broken in some interval of NSR. We show that encryptions with a nonvanishing linear component permit reconstructions with p ∞ > 0 for any µ > 1 and any γ < ∞, with p ∞ ∼ γ −1/2 as γ → ∞. In contrast, for the case of purely quadratic nonlinearity, for any ERP µ > 1 there exists a threshold NSR value γ c (µ) such that p ∞ = 0 for γ > γ c (µ) making the reconstruction impossible. The behaviour close to the threshold is given by p ∞ ∼ (γ c − γ) 3/4 and is controlled by the replica symmetry breaking mechanism. arXiv:1805.06982v1 [cond-mat.dis-nn] 17 May 2018 J 2 1 R 2