دانلود کتاب امضاهای کاربردی پساکوانتومی – FALCON و SOLMAE با پایتون

The current digital signature methods, such as RSA (Rivest-Shamir-Adleman), DSA (Digital Signature Algorithm), and ECDSA (Elliptic Curve Digital Signature Algorithm), are relatively straightforward in terms of mathematical understanding. While the signing and verification processes differ depending on the key used, the time required for these operations is nearly the same across these algorithms. However, in the era of quantum computing, cryptographic methods must defend against both current classical and future quantum attacks. Achieving this requires a deeper understanding of algebraic geometry, lattice theory, Gaussian sampling, and efficient polynomial computation techniques like FFT (Fast Fourier Transform) and NTT (Number Theoretic Transform), which are crucial for most lattice-based cryptosystems.
The FALCON algorithm, selected as a finalist in the NIST (National Institute of Standards and Technology) Post-Quantum Cryptography (PQC) standardization project after seven years of global evaluation, is a hash-and-sign digital signature scheme based on the NTRU (N-th degree TRUncated polynomial) lattice problem, within the GPV framework. Compared to other quantum-resistant signatures like DILITHIUM and SPHINCS+, FALCON offers a significantly smaller combined size for its public key and signature.
Following FALCON’s release, the SOLMAE algorithm was introduced in 2021. Like FALCON, SOLMAE is another hash-and-sign scheme that operates within the GPV (Genry Peikert Vaikuntanathan) framework but simplifies FALCON’s complex signing process. Both FALCON and SOLMAE have been implemented in Python, making them easier to understand and work with compared to other low-level programming languages. To enhance understanding of their functionality, we developed Python scripts that examine each algorithm step-by-step, breaking down the results and the underlying mathematical concepts.
This monograph serves as an introductory or educational textbook for undergrad-uate and graduate students, practitioners, engineers, and anyone interested in post-quantum digital signatures. The material aims to present complex cryptographic concepts in an accessible manner.