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A Verifiable Delay Function (VDF) is a function that takes a specifiedsequential time $T$ to be evaluated, but can be verified in$\Omega(\log{T})$-time. For meaningful security, $T$ can be at mostsubexponential in the security parameter $\lambda$ but has no lower bound. VDFsare useful in several applications ranging from randomness beacons tosustainable blockchains but are really rare in practice. The verification inall of these VDFs requires $\Omega(\lambda, \log{T})$ sequential time. Thispaper derives a verifiable delay function that is verifiable in$O(1)$-sequential time. The key observation is that the prior works usesubexponentially-hard algebraic assumptions for their sequentiality. On thecontrary, we derive our VDF from a polynomially-hard sequential assumptionnamely the time-lock puzzle over the group of known order. In particular, weshow that time-lock puzzle can be sequentially-hard even when the order of thegroup is known but the delay parameter is polynomially-bounded i.e., $T \le\mathtt{poly}(\lambda)$. As an add-on advantage, our VDF requires only onesequential squaring to verify. Thus, in our VDF, the sequential effort requiredfor verification is fixed and independent of the delay parameter $T$.

Single Squaring Verifiable Delay Function from Time-lock Puzzle in the Group of Known Order