# name
Elliptic curves, cryptographic proofs and signature schemes: a comprehensive analysis of the Pinocchio protocol and implementation frameworks

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Luis Victor Dieulefait

# metadata.dc.description.abstract[].value
This paper investigates the mathematical and cryptographic principles underlying elliptic curves and their critical role in modern secure communication systems. It begins with an exploration of elliptic curves and their group properties, emphasizing their utility in cryptography through problems like the discrete logarithm. The discussion transitions to the Pinocchio protocol, a zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK), detailing its use of Rank-1 Constraint Systems (R1CS), Quadratic Arithmetic Programs (QAPs), and
cryptographic commitments. The ﬁnal section delves into practical implementations, employing CIRCOM for circuit deﬁnition and testing, with speciﬁc applications to ECDSA and BLS signature schemes. Through this  comprehensive approach, the paper bridges theoretical cryptographic advancements with practical implementation, offering insights into the efﬁciency, security, and application of elliptic curve-based protocols.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Claudia Llamas Gómez, 2025

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Elliptic curves, cryptographic proofs and signature schemes: a comprehensive analysis of the Pinocchio protocol and implementation frameworks