• Top
    • Documentation
    • Books
    • Boolean-reasoning
    • Projects
      • Apt
      • Zfc
      • Acre
      • Milawa
      • Smtlink
      • Abnf
      • Vwsim
      • Isar
      • Wp-gen
      • Dimacs-reader
      • Pfcs
      • Legacy-defrstobj
      • Proof-checker-array
      • Soft
      • C
      • Farray
      • Rp-rewriter
      • Instant-runoff-voting
      • Imp-language
      • Sidekick
      • Leftist-trees
      • Java
      • Taspi
      • Bitcoin
      • Riscv
      • Des
      • Ethereum
      • X86isa
      • Sha-2
      • Yul
      • Zcash
      • Proof-checker-itp13
      • Regex
      • ACL2-programming-language
      • Json
      • Jfkr
      • Equational
      • Cryptography
      • Poseidon
      • Where-do-i-place-my-book
      • Axe
      • Bigmems
      • Builtins
      • Execloader
      • Aleo
      • Solidity
      • Paco
      • Concurrent-programs
      • Bls12-377-curves
        • Edwards-bls12
          • Edwards-bls12-pointp
          • Edwards-bls12-q
          • Edwards-bls12-d
          • Edwards-bls12-point->v
          • Edwards-bls12-point->u
          • Maybe-edwards-bls12-pointp
          • Edwards-bls12-add
          • Edwards-bls12-mul-fast
          • Edwards-bls12-rstar-pointp
          • Edwards-bls12-mul
          • Edwards-bls12-a
          • Edwards-bls12-r-pointp
          • Edwards-bls12-neg
          • Edwards-bls12-curve
          • Edwards-bls12-r
          • Edwards-bls12-h
          • Edwards-bls12-subgroup-prime
        • Bls12-377-domain-parameters
    • Debugging
    • Std
    • Proof-automation
    • Macro-libraries
    • ACL2
    • Interfacing-tools
    • Hardware-verification
    • Software-verification
    • Math
    • Testing-utilities
  • Bls12-377-curves

Edwards-bls12

The Edwards-BLS12 complete twisted Edwards elliptic curve.

We define the Edwards-BLS12 curve, as a constant value of the fixtype twisted-edwards-curve of twisted Edwards elliptic curves. We show that the curve is complete.

The prime and coefficients of Edwards-BLS12 are formalized as nullary functions. We keep disabled also their executable counterparts because we generally want to treat them as algebraic quantities in proofs; in particular, we want to avoid their combination into new constants by the prime field normalizing rules.

We also define various notions related to Edwards-BLS12, such as recognizers of points in the curve's group and subgroup.

Subtopics

Edwards-bls12-pointp
Recognize elements of Edwards-BLS12 curve.
Edwards-bls12-q
The Edwards-BLS12 base field prime F_q.
Edwards-bls12-d
The Edwards-BLS12 coefficient d
Edwards-bls12-point->v
The function \mathcal{V} in TODO
Edwards-bls12-point->u
The function \mathcal{U} in TODO
Maybe-edwards-bls12-pointp
Recognize Edwards-BLS12 points and nil.
Edwards-bls12-add
Group addition on Edwards-BLS12.
Edwards-bls12-mul-fast
Fast scalar multiplication on Edwards-BLS12.
Edwards-bls12-rstar-pointp
Recognize elements of r except the zero point.
Edwards-bls12-mul
Scalar multiplication on Edwards-BLS12.
Edwards-bls12-a
The Edwards-BLS12 coefficient a.
Edwards-bls12-r-pointp
Recognize elements of r.
Edwards-bls12-neg
Group point negation on Edwards-BLS12.
Edwards-bls12-curve
The Edwards-BLS12 curve
Edwards-bls12-r
The prime number that is the order of the large subgroup of Edwards-BLS12.
Edwards-bls12-h
The elliptic curve cofactor.
Edwards-bls12-subgroup-prime
A prime defined by defprime.