In 2003, Fischlin introduced the concept of progressive verification in cryptography to relate the error probability of a cryptographic verification procedure to its running time. It ensures that the verifier confidence in the validity of a verification procedure grows with the work it invests in the computation. Le, Kelkar and Kate recently revisited this approach for digital signatures and proposed a similar framework under the name of flexible signatures. We propose efficient probabilistic verification procedures for popular signature schemes in which the error probability of a verifier decreases exponentially with the verifier running time. We propose theoretical schemes for the RSA and ECDSA signatures based on some elegant idea proposed by Bernstein in 2000 and some additional tricks. We also present a general practical method, that makes use of efficient error-correcting codes, for signature schemes for which verification involves a matrix/vector multiplication.

在2003年，Fischlin引入了密码学中渐进验证的概念，以将密码验证过程的错误概率与其运行时间联系起来。它确保验证者对验证程序有效性的信心会随着它在计算上投入的工作而增长。Le，Kelkar和Kate最近重新探讨了这种用于数字签名的方法，并以弹性签名的名义提出了类似的框架。我们为流行的签名方案提出了有效的概率验证程序，其中验证者的错误概率随验证者运行时间呈指数下降。我们根据伯恩斯坦（Bernstein）在2000年提出的一些优雅构想和一些其他技巧，提出了针对RSA和ECDSA签名的理论方案。我们还提出了一种通用的实用方法，