Abstract

In this paper, we define expanded LRPC codes from LRPC codes with a decoding algorithm using the one of the underlying LRPC codes. Next, we propose to use these codes for cryptography by deriving two cryptosystems in a McEliece setting. in order to reduce the key sizes, we use a generator matrix in systematic form for the first scheme, and an m−$m-$$m-$ order quasi-cyclic LRPC code that we define for the second scheme. The obtained code has a very poor structure and is more likely to be a random linear code. Next, we give some security parameters and compare the key sizes of our public key with the key sizes of some cryptosystems.

摘要

在本文中，我们通过使用底层 LRPC 代码之一的解码算法从 LRPC 代码定义了扩展的 LRPC 代码。接下来，我们建议通过在 McEliece 设置中派生两个密码系统来将这些代码用于密码学。为了减少密钥大小，我们在第一个方案中使用系统形式的生成矩阵，以及米-$米-$$m-$我们为第二个方案定义的阶准循环 LRPC 代码。获得的代码结构很差，并且更有可能是随机线性代码。接下来，我们给出一些安全参数，并将我们的公钥的密钥大小与一些密码系统的密钥大小进行比较。