CAJ | 학술논문

TTM是一类三角形多变量公钥密码体制.该文经过分析2004年的TTM实例发现,该实例中存在大量的一阶线性化方程,而且对于给定的公钥,这些线性化方程都可以通过预计算得到.对于给定的合法密文,可以利用一阶线性化方程攻击方法在2~(19)个2~8 域上的运算内找到了其相应的明文.该方法与二阶线性化方程攻击方法相比,恢复明文的复杂度降低了2~(12)倍.计算机实验证实了上述结果.
TTM시일류삼각형다변량공약밀마체제.해문경과분석2004년적TTM실례발현,해실례중존재대량적일계선성화방정,이차대우급정적공약,저사선성화방정도가이통과예계산득도.대우급정적합법밀문,가이이용일계선성화방정공격방법재2~(19)개2~8 역상적운산내조도료기상응적명문.해방법여이계선성화방정공격방법상비,회복명문적복잡도강저료2~(12)배.계산궤실험증실료상술결과.
TTM is a type of Multivariate public key cryptosystem. By analyzing the instance of TTM proposed in 2004, it can be found that there are many first order linearization equations satisfied by the cipher in this scheme. For a given public key, all first order linearization equations can be found through precomputation. For any given ciphertext, the corresponding plaintext can be found in less than 2~(19) operations over a finite field of size 2~8 by linearization equation attack. This attack reduced complexity of recovering plaintext from 2~(31) to 2~(19) compare to second order linearization equation attack. The results above are further confirmed by computer experiments.