From bits to blocks Sample Clauses

From bits to blocks loss of generality that ℓest is a multiple of 𝑛. Then, for 𝑣 ∈ N satisfying bits(𝑣) ≤ ℓest, we define Instead of building some valid values’ prefix bit by bit, we may do so block by block. Assume without and, for any 1 ≤ 𝑖 ≤ 𝑛, block𝑖 = ℓest/𝑛. For 1 ≤ 𝑖 ≤ 𝑛, use block𝑖 (𝑣) to refer to block𝑖 . We will blocks(𝑣) := (block1, block2, . . . , block𝑛) such that bitsℓest (𝑣) = block1 block2 . . . block𝑛, / use the term block to refer to such sequences of ℓest 𝑛 bits. 𝑖 Following the outline of the warm-up approach, in iteration 𝑖, the parties hold valid ℓest-bit values 𝑣 having a common prefix prefix★ of 𝑖 − 1 blocks. In an attempt to extend prefix★ by one block prefix★, the parties join a BA protocol ΠℓBA (for long messages) with block𝑖 (𝑣) as input. 𝑖 𝑖 When the parties agree on a block. If the parties agree on a block prefix★, the honest parties holding block𝑖 ≠ prefix★ should update their values 𝑣 to match the prefix agreed upon. However, unless all honest parties hold block𝑖 = prefix★, prefix★ may be a block proposed by a corrupted 𝑖 𝑖 party, forcing the updated values outside the honest range. To prevent this, we make use of the special symbol ⊥, and we require ΠℓBA to achieve an additional property, as defined below.