Supersingular Isogeny Key Encapsulation: SIKEp751 & SIKEp610 & SIKEp503 & SIKEp434
written in C language
=======================================================================
    
This software library contains faster software implementation of the SIKE protocol based on a new data representation for SIKEp434, SIKEp503, SIKEp610, SIKEp751. They can be found under "/src/P434_uRadix", "/src/P503_uRadix", "/src/P610_uRadix", "/src/P751_uRadix", where the files for finite field arithmetic computing are compiled as object files.
The referred implementations for SIKEp434, SIKEp503, SIKEp610, SIKEp751 based on the Montgomery reduction are also attached. They are under "/src/P434_Mont", "/src/P503_Mont", "/src/P610_Mont", "/src/P751_Mont". 

* SIKEp434: matching the post-quantum security of AES128 (level 1).
* SIKEp503: matching the post-quantum security of SHA3-256 (level 2).
* SIKEp610: matching the post-quantum security of AES192 (level 3).
* SIKEp751: matching the post-quantum security of AES256 (level 5).

## Contents
* [`KAT folder`](KAT/): Known Answer Test (KAT) files for the KEM.
* [`src folder`](src/): C and header files.
* [`random folder`](src/random/): random bytes function using the system random number generator.
* [`sha3 folder`](src/sha3/): SHAKE256 implementation.  
* [`Test folder`](tests/): test files.   
* [`referred implementation for p751 base on the Montgomery reduction`](src/P751_Mont/P751/generic/): implementation of the field arithmetic over the prime p751 in portable C based on the Montgomery reduction.
* [`referred implementation for p610 base on the Montgomery reduction`](src/P610_Mont/P610/generic/): implementation of the field arithmetic over the prime p610 in portable C based on the Montgomery reduction.
* [`referred implementation for p503 base on the Montgomery reduction`](src/P503_Mont/P503/generic/): implementation of the field arithmetic over the prime p503 in portable C based on the Montgomery reduction.
* [`referred implementation for p434 base on the Montgomery reduction`](src/P434_Mont/P434/generic/): implementation of the field arithmetic over the prime p434 in portable C based on the Montgomery reduction.

* [`proposed implementation for p751 base on a new data representation`](src/P751_uRadix/P751/generic/): implementation of the field arithmetic over the prime p751 in portable C based on a new data representation.
* [`proposed implementation for p610 base on a new data representation`](src/P610_uRadix/P610/generic/): implementation of the field arithmetic over the prime p610 in portable C based on a new data representation.
* [`proposed implementation for p503 base on a new data representation`](src/P503_uRadix/P503/generic/): implementation of the field arithmetic over the prime p503 in portable C based on a new data representation.
* [`proposed implementation for p434 base on a new data representation`](src/P434_uRadix/P434/generic/): implementation of the field arithmetic over the prime p434 in portable C based on a new data representation.

## Instructions for Linux (64-bit operating system)
1.
$ cd generic-master
2.
$ make clean
3.
$ make
4.
$ cd sike

Testing and benchmarking results are obtained by running:

$ ./test_KEM_P434_Mont
$ ./test_KEM_P503_Mont
$ ./test_KEM_P610_Mont
$ ./test_KEM_P751_Mont
$ ./test_KEM_P434_uRadix
$ ./test_KEM_P503_uRadix
$ ./test_KEM_P610_uRadix
$ ./test_KEM_P751_uRadix

To run the implementations against the KATs provided in the KAT folder,
execute:

$ ./PQCtestKAT_kem_P434_Mont
$ ./PQCtestKAT_kem_P503_Mont
$ ./PQCtestKAT_kem_P610_Mont
$ ./PQCtestKAT_kem_P751_Mont
$ ./PQCtestKAT_kem_P434_uRadix
$ ./PQCtestKAT_kem_P503_uRadix
$ ./PQCtestKAT_kem_P610_uRadix
$ ./PQCtestKAT_kem_P751_uRadix

## Example results on the Intel(R) Xeon(R) CPU E5-2690@ 2.90GHz

Turbo Boost option disabled:

$ ./test_KEM_P434_Mont
  Key generation runs in .......................................   66056313 cycles
  Encapsulation runs in ........................................  106052319 cycles
  Decapsulation runs in ........................................  113185503 cycles

$ ./test_KEM_P503_Mont
  Key generation runs in .......................................   99349280 cycles
  Encapsulation runs in ........................................  163598002 cycles
  Decapsulation runs in ........................................  174144615 cycles
  
$ ./test_KEM_P610_Mont
  Key generation runs in .......................................  186213290 cycles
  Encapsulation runs in ........................................  342070689 cycles
  Decapsulation runs in ........................................  344433945 cycles

$ ./test_KEM_P751_Mont
  Key generation runs in .......................................  330359813 cycles
  Encapsulation runs in ........................................  534684859 cycles
  Decapsulation runs in ........................................  574877203 cycles

$ ./test_KEM_P434_uRadix
  Key generation runs in .......................................   44205016 cycles
  Encapsulation runs in ........................................   71809157 cycles
  Decapsulation runs in ........................................   76820145 cycles

$ ./test_KEM_P503_uRadix
  Key generation runs in .......................................   61784626 cycles
  Encapsulation runs in ........................................  101787564 cycles
  Decapsulation runs in ........................................  108103000 cycles
  
$ ./test_KEM_P610_uRadix
  Key generation runs in .......................................   92155578 cycles
  Encapsulation runs in ........................................  168786347 cycles
  Decapsulation runs in ........................................  170012117 cycles

$ ./test_KEM_P751_uRadix
  Key generation runs in .......................................  199942406 cycles
  Encapsulation runs in ........................................  324438988 cycles
  Decapsulation runs in ........................................  347941364 cycles