基于深度学习的随机性检验策略研究

Research on test strategy for randomness based on deep learning

为了获得更好的检验效果,对基于深度学习的随机性检验策略进行了研究,包括2021年欧密会提出的批均化策略和数据单元大小的选择策略。通过给出基于深度学习方法的随机性统计检验模型,理论推导得到2个检验策略的统计量分布和检验势表达,并指出:1)批均化策略虽然能够提升模型预测准确率,但在统计上容易造成第二类错误概率的增大,反而降低了检验势;2)一般情况下深度学习模型的数据单元越小,取得的检验势越高。基于以上认识,提出了一种新的比特级深度学习模型用于随机性统计检验。该模型应用于线性同余发生器(LCG)算法,相比之前工作,参数量减少至1/80,取得预测优势所需数据减少了50%以上;拓展应用于5~7轮Speck算法获得了明显的预测优势,与Gohr模型相比,参数量减少至1/10~1/20。

In order to achieve better test performance,researches on the randomness test strategies based on deep learning were conducted,including the batch average strategy proposed by EUROCRYPT 2021 and the selection strategy for data unit size.By introducing the randomness statistical test model based on deep learning methods,the statistical distribution and test power expression of two test strategies were theoretically derived,and it was pointed out that:(i)the batch average strategy could amplify the prediction accuracy of the model,but it was prone to an increase in the probability of the second type of error in statistics,instead reducing the statistical test power;(ii)the smaller data units of the deep model generally obtained the more powerful statistical tests.Based on the above understanding,a new bit-level deep learning model was proposed for randomness statistical tests,which gained the advantage of prediction with 80 times fewer parameters and 50%samples,compared with the previous work on linear congruent generator(LCG)algorithm,and achieved significant prediction advantages with 10~20 times fewer parameters by extending the model to apply to 5~7 rounds of Speck,compared with the model proposed by Gohr.