论文标题
加密操作员计算：一种用于加密数据计算的新方案
Encrypted Operator Computing: a novel scheme for computation on encrypted data
论文作者
论文摘要
我们在加密数据（EOC）上引入了一种新的计算方法，以替代完全同构加密（FHE）。给定一个明文矢量$ | {x} \ rangle $，$ x \ in \ {0,1 \}^n $，以及作为运算符$ \ hat f $，$ \ hat f $，$ f（x）$的函数$ f（x）$ （电路）$ \ hat {f}^e = \ hat e \; \ hat f \; \ hat {e}^{ - 1} $在加密数据上实现计算，$ \ hat e | {x} \ rangle $。 The construction of EOC hinges on the existence of a two-stage NC$^1$ reversible-circuit-based IND-CCA2 cipher $\hat{E} = \hat{N} \hat{L}$, where $\hat{L}$ and $\hat{N}$ represent, respectively, linear and non-linear NC$^1$ tree-structured circuits of 3-bit可逆大门。我们对这种NC $^1 $密码做出并激励安全假设。此外，我们通过证明：（a）$ f $的每个门与$ \ hat {l} $的共轭，建立了混淆电路的多项式复杂性，评估器$ o（\ hat {f}^e）$。 （b）随后与$ \ hat {n} $的结合产生``芯片'''''''''''''''''''''''''''''''''''''''$ n $ - unput/$ n $ output可逆函数，输出表示为多项式大小的有序二进制二进制决策图（OBDDS）。单个芯片的安全性连接到依赖于多大尺寸OBDD的最佳可能混淆器的概念，并且OBDD是暴露该功能但隐藏芯片门的正常形式的事实。我们猜想在构建$ f^e $的$ \ hat {n} $层之间添加了随机对nots，这是一种类似于AES的AddRoundKey回合的设备，可确保评估员的安全性。我们还提出了对不对称加密的概括。
We introduce a new approach to computation on encrypted data -- Encrypted Operator Computing (EOC) -- as an alternative to Fully Homomorphic Encryption (FHE). Given a plaintext vector $|{x}\rangle$, $x\in \{0,1\}^n$, and a function $F(x)$ represented as an operator $\hat F$, $\hat F\;|{x}\rangle = |{F(x)}\rangle$, the EOC scheme is based on obfuscating the conjugated operator (circuit) $\hat{F}^E = \hat E\;\hat F\;\hat{E}^{-1}$ that implements computation on encrypted data, $\hat E |{x}\rangle$. The construction of EOC hinges on the existence of a two-stage NC$^1$ reversible-circuit-based IND-CCA2 cipher $\hat{E} = \hat{N} \hat{L}$, where $\hat{L}$ and $\hat{N}$ represent, respectively, linear and non-linear NC$^1$ tree-structured circuits of 3-bit reversible gates. We make and motivate security assumptions about such a NC$^1$ cipher. Furthermore, we establish the polynomial complexity of the obfuscated circuit, the evaluator $O(\hat{F}^E)$, by proving that: (a) conjugation of each gate of $F$ with $\hat{L}$ yields a polynomial number of gates; and (b) the subsequent conjugation with $\hat{N}$ yields a polynomial number of ``chips,'' $n$-input/$n$-output reversible functions, with outputs expressed as polynomial-sized ordered Binary Decision Diagrams (OBDDs). The security of individual chips is connected to the notion of Best Possible Obfuscators which relies on poly-size OBDDs and the fact that OBDDs are normal forms that expose the functionality but hide the gate implementation of the chip. We conjecture that the addition of random pairs of NOTs between layers of $\hat{N}$ during the construction of $F^E$, a device analogous to the AddRoundKey rounds of AES, ensures the security of the the evaluator. We also present a generalization to asymmetric encryption.
