Properties of sigma protocols are invariant under parallel composition 咋理解
原文应该是这个吧 http://www.cs.au.dk/~ivan/Sigma.pdf
第三页
Lemma 1. The properties of Σ-protocols are invariant under parallelcomposition, for instance repeating a Σ-protocol for R twice in parallelproduces a new Σ-protocol for R with challenge length 2t.我的理解是，如果并行进行若干个Sigma Protocol, 则新Sigmal Protocol的性质 (比如定义里提到的123)并不会发生改变。
Lemma里说，如果并行两个，实际上就是让challenge的有效长度延长一倍，因为P得两个长度为t的challenge都解决了才能完成这个proof.
三个性质：(第三页Definition 1)
1.
P is of the above 3-move form, and we have completeness: if P, Vfollow the protocol on input x and private input w to P where (x, w) ∈R, the verifier always accepts.这个在并行时肯定满足, P只要知道w，都可以回答
2. 从两个正确的回答可以算出w
并行运行两次，只要 e != e\u0026#39;, 从两个答案里的确可以算出w
3.
【Properties of sigma protocols are invariant under parallel composition 咋理解】 There exists a polynomial-time simulator M, which on input x and arandom e outputs an accepting conversation of the form (a, e, z), withthe same probability distribution as conversations between the honestP, V on input x. This is sometimes called special honest-verifier zeroknowledge.
这个也好验证, 把2t长度的e分成前后两段长度为t的e1，e2，就可以做出（a1,e1,z1）,(a2,e2,z2), 正好是并行的两个conversation的内容。其实参考Lemma 2和后面的proof也可以加深理解。
