Biblio

We present a method for key compression in quantumresistant isogeny-based cryptosystems, which allows a reduction in and transmission costs of per-party public information by a factor of two, with no e ect on security. We achieve this reduction by associating a canonical choice of elliptic curve to each j-invariant, and representing elements on the curve as linear combinations with respect to a canonical choice of basis. This method of compressing public information can be applied to numerous isogeny-based protocols, such as key exchange, zero-knowledge identi cation, and public-key encryption. We performed personal computer and ARM implementations of the key exchange with compression and decompression in C and provided timing results, showing the computational cost of key compression and decompression at various security levels. Our results show that isogeny-based cryptosystems achieve by far the smallest possible key sizes among all existing families of post-quantum cryptosystems at practical security levels; e.g. 3073-bit public keys at the quantum 128-bit security level, comparable to (non-quantum) RSA key sizes.

Efficient implementation of double point multiplication is crucial for elliptic curve cryptographic systems. We propose efficient algorithms and architectures for the computation of double point multiplication on binary elliptic curves and provide a comparative analysis of their performance for 112-bit security level. To the best of our knowledge, this is the first work in the literature which considers the design and implementation of simultaneous computation of double point multiplication. We first provide algorithmics for the three main double point multiplication methods. Then, we perform data-flow analysis and propose hardware architectures for the presented algorithms. Finally, we implement the proposed state-of-the-art architectures on FPGA platform for the comparison purposes and report the area and timing results. Our results indicate that differential addition chain based algorithms are better suited to compute double point multiplication over binary elliptic curves for high performance applications.

We present a method for key compression in quantumresistant isogeny-based cryptosystems, which allows a reduction in and transmission costs of per-party public information by a factor of two, with no e ect on security. We achieve this reduction by associating a canonical choice of elliptic curve to each j-invariant, and representing elements on the curve as linear combinations with respect to a canonical choice of basis. This method of compressing public information can be applied to numerous isogeny-based protocols, such as key exchange, zero-knowledge identi cation, and public-key encryption. We performed personal computer and ARM implementations of the key exchange with compression and decompression in C and provided timing results, showing the computational cost of key compression and decompression at various security levels. Our results show that isogeny-based cryptosystems achieve by far the smallest possible key sizes among all existing families of post-quantum cryptosystems at practical security levels; e.g. 3073-bit public keys at the quantum 128-bit security level, comparable to (non-quantum) RSA key sizes.