03/03/2022:

BLS12-377 / BW6 <- Justin talks about Zexe , 2chain of curve

$E_1(F_q)$ of order $r$ $E_2(F_t)$ of order $q$ <-- circuits in $F_q$, means I can express group operations efficiently, $E_1(F_q) + E_1(F_q)$

$G_t$ is in $F_q^{12}$

Benchmark

2 Circuits for https://github.com/nikkolasg/grothan/blob/main/src/lib.rs

• Multiplication of two GT elements
  • 66 constraints
• Scalar multiplication of one scalar and GT elements
  • 39409 constraints
• Enforcing equality:
  • 12 constraints

IPP verifcation

• $T_i = T_l^x * T * T_r^{x^{-1}}$
• U
• Z

Per iteration of the loop

• 2 GT multiplication * 3 ⇒ 6 Gt MUL
• 6 Scalr mul

In total:

6 * log(n) * GT_MUL + 6 * log(n) * Scalar_mul

for n = 2**30