A C and ARM64 finite field arithmetic library
Implemented random number generation, modular reduction, addition, subtraction, negation, multiplication, multiplicative inverse, Legendre symbol, square root in some prime fields of sizes from 64 bits to 512 bits.
Implementation is constant-time, constant memory access with no branching and input independent.
EASIEST WAY TO RUN
You can do all benchmarks and tests by giving execution priviledges to the script go.sh
chmod +x go.sh
This script cleans, compiles and runs the program. Make sure execution priviledges are provided for the directory.
./go.sh Makes all prime sizes and runs arithmetic tests and benchmarks
./go.sh FAST Makes all prime sizes with ARM64 assebly, and runs all tests and benchmark
./go.sh X Makes X bit prime, runs all tests and benchmark
./go.sh X FAST Makes X bit prime with ARM64 assembly, runs all tests and benchmarks
./go.sh ALT Makes all prime sizes and runs arithmetic tests and benchmarks with an alternative prime for each prime size
./go.sh ALT X ./go.sh ALT FAST ./go.sh ALT X FAST As above with appropriate modifications.
Run make which will compile arithmetic tests and benchmarks for 64,128,192,256,512 bit sized prime fields. The executables are arith64, arith128, arith192, arith256, arith512..
By running make arith64 you will only compile the 64 bit prime arithmetic (and respectively for 128, 192, 256, 512)
By running make arith64 OPT_LEVEL=FAST you will compile ARM64 assembly code which is optimised. It speeds up the multiplications, modular reduction, etc. For other prime sizes use arith128, etc. respectively.
By running make arith64 ALT_PRIMES=ALT the compilation takes place by using alternative prime values. Different prime sizes and assembly can be made with corresponding flags.
Primes:
ORIGINAL
p = 2^61 - 1 = 0x1FFFFFFFFFFFFFFF
ALT
p = 2^64 - 59 = 0xFFFFFFFFFFFFFFC5
ORIGINAL
p = 2^127 - 1 = 0x7FFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF
ALT
p = 2^128 - 173 = 0xFFFFFFFFFFFFFFFF FFFFFFFFFFFFFF53
ORIGINAL
p = 2^192 - 237 = 0xFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF FFFFFFFFFFFFFF13
ALT
p = 2^191 - 19 = 0x7FFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFED
ORIGINAL
p = 2^255 - 19 = 0x7FFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFED
ALT
p = 2^256 - 2^224 + 2^192 + 2^96 - 1 = 0xFFFFFFFF00000001 0000000000000000 00000000FFFFFFFF FFFFFFFFFFFFFFFF
ORIGINAL
p = 2^512 - 2^256 + 2^192 - 2^128 - 1 = 0xFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF 0000000000000000 FFFFFFFFFFFFFFFE FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF
ALT
p = 2^511 - 2^320 + 1 = 0x7FFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF 0000000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000001
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