Multi scalar multiplications

Algorithms and methods

• Fast Multi-scalar Multiplication Methods on Elliptic Curves with Precomputation Strategy Using Montgomery Trick
• Faster batch forgery identification See section 4 for MSM, bucket method
• Pippenger’s exponentiation algorithm - Bernstein
• Efficient multi-exponentiation
  • implementation in Python
• Multi-scalar multiplication: state of the art & new ideas with Gus Gutoski
• Improved Fast exponentiations - Bodo Moller
• Fast exponentiation with precomputation - Brickell Gordon et al
• Matter labs -ALgorithms
• Ryah Henry - Thesis
• Efficient Multi exponentiation: Bucket method - Bootle
• MSM tricks

Implementations

• pipezk
• MSM with FPGA -Connor Masterson thesis
• PipeMSM
• EdMSM
• CycloneMSM
• Cuzk
• Zprize MSM implementations