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Filters: Author is Koziel, Brian  [Clear All Filters]
2017-11-27
Leonardi, Christopher, Koziel, Brian, Kalach, Kassem, Jao, David, Azarderakhsh, Reza.  2016.  Key Compression for Isogeny-Based Cryptosystems.

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.

2017-05-22
Azarderakhsh, Reza, Jao, David, Kalach, Kassem, Koziel, Brian, Leonardi, Christopher.  2016.  Key Compression for Isogeny-Based Cryptosystems. Proceedings of the 3rd ACM International Workshop on ASIA Public-Key Cryptography. :1–10.

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.