Today, we see a large dependence on systems developed with cryptography. Especially in terms of public key cryptosystems, which are widely used on the Internet. However, public key cryptography was threatened and new sources began to be investigated when Shor in 1997 developed a polynomial time algorithm for factoring integers and to compute the discrete logarithm with a quantum computer. In this context, Patarin proposed Hidden Field Equations (HFE), a trapdoor based on 𝓜𝓜𝓜𝓜 (𝓜𝓜ultivariate 𝓠𝓠uadratic) and IP (Isomorphism of Polynomials) problems. Such problems are not affected by the Shor algorithm, moreover 𝓜𝓜𝓜𝓜 Problem was proved by Patarin and Goubin to be NP-complete. Despite the basic HFE has been broken, there are variants that are secure, obtained by a generic modification. The Quartz – digital signature scheme based on HFEv-, with special choice of parameters – is a good example of this resistance to algebraic attacks aimed at the recovery of the private key, because even today it remains secure. Furthermore, it also generates short signatures. However, Joux and Martinet, based on axioms of Birthday Paradox Attack, proved that Quartz is malleable, showing that if the adversary has a valid pair (message, signature), he can get a second signature with 𝟐𝟐𝟓𝟓𝟓𝟓 computations and 𝟐𝟐𝟓𝟓𝟓𝟓 calls to the signing oracle, so that the estimated current security standards are at least 𝟐𝟐𝟏𝟏𝟏𝟏𝟏𝟏. Thus, based on Quartz, we present a new digital signature scheme, achieving the adaptive chosen message attacks that make calls to the random oracle, with a security level estimated at 𝟐𝟐𝟏𝟏𝟏𝟏𝟏𝟏. Our cryptosystem also provides an efficiency gain in signature verification algorithm and vector initializations that will be used for signing and verification algorithms. Furthermore we provide an implementation of Original Quartz and Enhanced Quartz in the Java programming language.