基于低密度生成矩阵码的签密方案

基于编码的密码系统具备抵抗量子计算的天然优势。针对传统的基于Goppa码构造的密码方案存在密文扩展率大和密钥量大的问题，利用低密度生成矩阵 （LDGM） 码和哈希函数构造了一个可证明安全的签密方案。LDGM码的生成矩阵是稀疏的，能有效减小数据量，哈希函数计算效率很高。方案满足随机预言机下的适应性选择密文攻击下的不可区分性（IND-CCA2）和选择消息攻击下存在性不可伪造（EUF-CMA）安全。在保证数据机密性和完整性的同时，与传统的先签名后加密的方法相比，输出密文总量减少了25%；与“一石二鸟”和SCS签密方案相比，计算效率有较大提高。

Signcryption scheme based on low-density generator-matrix code

Code-based cryptography has natural advantage to resist the attack from quantum computers. Considering the long ciphertext length and the large key size of the traditional Goppa-codes-based cryptography, Low-Density Generator-Matrix (LDGM) code and hash function were used to construct a provably secure signcryption scheme. The generator matrix of LDGM code is sparse, so it can effectively reduce the amount of data, and the hash function is of high computation efficiency. It satisfies IND-CCA2 (INDistinguishability under Adaptive Chosen Ciphertext Attacks) and EUF-CMA (Existential UnForgeability under Chosen Message Attacks) security under random oracle model. As it guarantees data confidentiality and integrality, the ciphertext is reduced by 25% compared with the traditional case of "sign then encrypt"; compared with the "two birds one stone" and the SCS signcryptions, its computational efficiency gets significant improvement.