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Post-Quantum Group Authenticated Key Exchange protocol with the LibOQS library

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Post-Quantum Group Authenticated Key Exchange protocol with the LibOQS library

CMake Build Matrix

This repository implements a Post-Quantum Group Authenticated Key Exchange protocol based on design from[1] with the FSXY transformation[2], on Classic McEliece, Kyber, NTRU, and Saber and a compares their performance.

What are Classic McEliece, Kyber, NTRU, and Saber?

Classic McEliece, Kyber, NTRU, and Saber are finalist key encapsulation mechanisms (KEM) of the NIST Post-Quantum Criptography standardization project.

Dependencies

Supported algorithms

Click to expand!
* Classic-McEliece-348864
* Classic-McEliece-348864f
* Classic-McEliece-460896
* Classic-McEliece-460896f
* Classic-McEliece-6688128
* Classic-McEliece-6688128f
* Classic-McEliece-6960119
* Classic-McEliece-6960119f
* Classic-McEliece-8192128
* Classic-McEliece-8192128f
* Kyber512
* Kyber768
* Kyber1024
* NTRU-HPS-2048-509
* NTRU-HPS-2048-677
* NTRU-HPS-4096-821
* NTRU-HRSS-701
* LightSaber-KEM
* Saber-KEM
* FireSaber-KEM

Binaries

Download the latest version from Releases.

How to compile on Ubuntu

  1. Clone liboqs and build forked liboqs.
bash .github/liboqs.sh
  1. Run cmake.
mkdir build && cd build
cmake ..
make
  1. Run tests
ctest

Run GAKE binary

./bin/test_gake <number of parties> <KEM name> [-v]

Example 1

./bin/test_gake 10 LightSaber-KEM
Round 1-2
Round 3
Round 4
All keys are equal!
Session key: 373b7c6c33a1f93dc7ed1f09ec384e499c632381c100b43997e1724826b1753a
Session id:  0f5f1d1088565f156afd925251e0aaf5840489756b399e798ca0dd0232dd8aad


Time stats
	Init time      : 0.001s (8.00%)
	Round 1-2 time : 0.004s (58.92%)
	Round 3 time   : 0.000s (4.44%)
	Round 4 time   : 0.002s (28.64%)
	Total time     : 0.007s (100.00%)

Example 2

Click to expand!
./bin/test_gake 3 LightSaber-KEM -v
Party 0
	Public key:  6f3780906f6dd7543d01...cf24633139725f08d864
	Secret key:  ffffff0b000000000040...676154f6d13f7c6661b0
	Left key:    00000000000000000000...00000000000000000000
	Right key:   00000000000000000000...00000000000000000000
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 00000000000000000000...00000000000000000000
		X1: 00000000000000000000...00000000000000000000
		X2: 00000000000000000000...00000000000000000000
	Coins:
		r0: 00000000000000000000...00000000000000000000
		r1: 00000000000000000000...00000000000000000000
		r2: 00000000000000000000...00000000000000000000
	Commitments:
		c0: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c1: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c2: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Party 1
	Public key:  aa342e917ec5bd94532e...7091533d2b99b6fa0e53
	Secret key:  01e0ff0f8000f0fffbbf...121d26073a42d3b2bc7e
	Left key:    00000000000000000000...00000000000000000000
	Right key:   00000000000000000000...00000000000000000000
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 00000000000000000000...00000000000000000000
		X1: 00000000000000000000...00000000000000000000
		X2: 00000000000000000000...00000000000000000000
	Coins:
		r0: 00000000000000000000...00000000000000000000
		r1: 00000000000000000000...00000000000000000000
		r2: 00000000000000000000...00000000000000000000
	Commitments:
		c0: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c1: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c2: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Party 2
	Public key:  04b9d39a88b2fa2fa9ca...3d1cb561c8e9c59bcb14
	Secret key:  004000008000400000c0...95bc6fb21854991fc9ac
	Left key:    00000000000000000000...00000000000000000000
	Right key:   00000000000000000000...00000000000000000000
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 00000000000000000000...00000000000000000000
		X1: 00000000000000000000...00000000000000000000
		X2: 00000000000000000000...00000000000000000000
	Coins:
		r0: 00000000000000000000...00000000000000000000
		r1: 00000000000000000000...00000000000000000000
		r2: 00000000000000000000...00000000000000000000
	Commitments:
		c0: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c1: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c2: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Round 1-2
Party 0
	Public key:  6f3780906f6dd7543d01...cf24633139725f08d864
	Secret key:  ffffff0b000000000040...676154f6d13f7c6661b0
	Left key:    b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
	Right key:   cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 00000000000000000000...00000000000000000000
		X1: 00000000000000000000...00000000000000000000
		X2: 00000000000000000000...00000000000000000000
	Coins:
		r0: 00000000000000000000...00000000000000000000
		r1: 00000000000000000000...00000000000000000000
		r2: 00000000000000000000...00000000000000000000
	Commitments:
		c0: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c1: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c2: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Party 1
	Public key:  aa342e917ec5bd94532e...7091533d2b99b6fa0e53
	Secret key:  01e0ff0f8000f0fffbbf...121d26073a42d3b2bc7e
	Left key:    cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
	Right key:   8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 00000000000000000000...00000000000000000000
		X1: 00000000000000000000...00000000000000000000
		X2: 00000000000000000000...00000000000000000000
	Coins:
		r0: 00000000000000000000...00000000000000000000
		r1: 00000000000000000000...00000000000000000000
		r2: 00000000000000000000...00000000000000000000
	Commitments:
		c0: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c1: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c2: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Party 2
	Public key:  04b9d39a88b2fa2fa9ca...3d1cb561c8e9c59bcb14
	Secret key:  004000008000400000c0...95bc6fb21854991fc9ac
	Left key:    8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Right key:   b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 00000000000000000000...00000000000000000000
		X1: 00000000000000000000...00000000000000000000
		X2: 00000000000000000000...00000000000000000000
	Coins:
		r0: 00000000000000000000...00000000000000000000
		r1: 00000000000000000000...00000000000000000000
		r2: 00000000000000000000...00000000000000000000
	Commitments:
		c0: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c1: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
		c2: 00000000000000000000...00000000000000000000|00000000000000000000...00000000000000000000|00000000000000000000000000000000
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Round 3
Party 0
	Public key:  6f3780906f6dd7543d01...cf24633139725f08d864
	Secret key:  ffffff0b000000000040...676154f6d13f7c6661b0
	Left key:    b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
	Right key:   cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 7980e2bc73fc7770e4bb...95df8ee7896c29c29624
		X1: 473105cba0ddeb665b0f...23dae373472bd11ac353
		X2: 3eb1e777d3219c16bfb4...b6056d94ce47f8d85577
	Coins:
		r0: 40654d6ad9f8fa0e9e88...28498a3717497d50379a
		r1: dcf216a2f003095e2613...76e851e19a0a630239bb
		r2: 5517f02ba5933ae3e4c5...6e65812e47ac554f7375
	Commitments:
		c0: 48295f823c7aba107c87...a3bd748e2b88edd18489|fcc6fa8d8de0a5df95ca...6422c2222d514c65c02a|8b01e37e50889f0596aab0efcdd95309
		c1: fb4ddba67a0e6ef3dc7f...3b6c31d82921765b5b18|47abb0c7edd90f26f67b...be7c5c0eb9c9fc6e7bd8|bd4206864e76acc8485496674b2f90c5
		c2: 084828fdeea4cffa634a...703d96c71fb7193a1509|89d3d7063f6374a761c2...f11b9f458789f0b3410c|00ddcf95551ff54fc1b3693d236e241e
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Party 1
	Public key:  aa342e917ec5bd94532e...7091533d2b99b6fa0e53
	Secret key:  01e0ff0f8000f0fffbbf...121d26073a42d3b2bc7e
	Left key:    cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
	Right key:   8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 7980e2bc73fc7770e4bb...95df8ee7896c29c29624
		X1: 473105cba0ddeb665b0f...23dae373472bd11ac353
		X2: 3eb1e777d3219c16bfb4...b6056d94ce47f8d85577
	Coins:
		r0: 40654d6ad9f8fa0e9e88...28498a3717497d50379a
		r1: dcf216a2f003095e2613...76e851e19a0a630239bb
		r2: 5517f02ba5933ae3e4c5...6e65812e47ac554f7375
	Commitments:
		c0: 48295f823c7aba107c87...a3bd748e2b88edd18489|fcc6fa8d8de0a5df95ca...6422c2222d514c65c02a|8b01e37e50889f0596aab0efcdd95309
		c1: fb4ddba67a0e6ef3dc7f...3b6c31d82921765b5b18|47abb0c7edd90f26f67b...be7c5c0eb9c9fc6e7bd8|bd4206864e76acc8485496674b2f90c5
		c2: 084828fdeea4cffa634a...703d96c71fb7193a1509|89d3d7063f6374a761c2...f11b9f458789f0b3410c|00ddcf95551ff54fc1b3693d236e241e
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Party 2
	Public key:  04b9d39a88b2fa2fa9ca...3d1cb561c8e9c59bcb14
	Secret key:  004000008000400000c0...95bc6fb21854991fc9ac
	Left key:    8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Right key:   b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
	Session id:  00000000000000000000...00000000000000000000
	Session key: 00000000000000000000...00000000000000000000
	X:
		X0: 7980e2bc73fc7770e4bb...95df8ee7896c29c29624
		X1: 473105cba0ddeb665b0f...23dae373472bd11ac353
		X2: 3eb1e777d3219c16bfb4...b6056d94ce47f8d85577
	Coins:
		r0: 40654d6ad9f8fa0e9e88...28498a3717497d50379a
		r1: dcf216a2f003095e2613...76e851e19a0a630239bb
		r2: 5517f02ba5933ae3e4c5...6e65812e47ac554f7375
	Commitments:
		c0: 48295f823c7aba107c87...a3bd748e2b88edd18489|fcc6fa8d8de0a5df95ca...6422c2222d514c65c02a|8b01e37e50889f0596aab0efcdd95309
		c1: fb4ddba67a0e6ef3dc7f...3b6c31d82921765b5b18|47abb0c7edd90f26f67b...be7c5c0eb9c9fc6e7bd8|bd4206864e76acc8485496674b2f90c5
		c2: 084828fdeea4cffa634a...703d96c71fb7193a1509|89d3d7063f6374a761c2...f11b9f458789f0b3410c|00ddcf95551ff54fc1b3693d236e241e
	Master Key:
		k0: 00000000000000000000...00000000000000000000
		k1: 00000000000000000000...00000000000000000000
		k2: 00000000000000000000...00000000000000000000
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   0
	Terminated: 0
Round 4
	Party 0
		Xi are zero!
		Commitments are correct!
	Party 1
		Xi are zero!
		Commitments are correct!
	Party 2
		Xi are zero!
		Commitments are correct!
Party 0
	Public key:  6f3780906f6dd7543d01...cf24633139725f08d864
	Secret key:  ffffff0b000000000040...676154f6d13f7c6661b0
	Left key:    b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
	Right key:   cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
	Session id:  335683f5d6f68c07f403...9ff0ec0666c8aa758e9f
	Session key: b9543925d432aa649f44...dc567363cbf681ba4dec
	X:
		X0: 7980e2bc73fc7770e4bb...95df8ee7896c29c29624
		X1: 473105cba0ddeb665b0f...23dae373472bd11ac353
		X2: 3eb1e777d3219c16bfb4...b6056d94ce47f8d85577
	Coins:
		r0: 40654d6ad9f8fa0e9e88...28498a3717497d50379a
		r1: dcf216a2f003095e2613...76e851e19a0a630239bb
		r2: 5517f02ba5933ae3e4c5...6e65812e47ac554f7375
	Commitments:
		c0: 48295f823c7aba107c87...a3bd748e2b88edd18489|fcc6fa8d8de0a5df95ca...6422c2222d514c65c02a|8b01e37e50889f0596aab0efcdd95309
		c1: fb4ddba67a0e6ef3dc7f...3b6c31d82921765b5b18|47abb0c7edd90f26f67b...be7c5c0eb9c9fc6e7bd8|bd4206864e76acc8485496674b2f90c5
		c2: 084828fdeea4cffa634a...703d96c71fb7193a1509|89d3d7063f6374a761c2...f11b9f458789f0b3410c|00ddcf95551ff54fc1b3693d236e241e
	Master Key:
		k0: b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
		k1: cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
		k2: 8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   1
	Terminated: 1
Party 1
	Public key:  aa342e917ec5bd94532e...7091533d2b99b6fa0e53
	Secret key:  01e0ff0f8000f0fffbbf...121d26073a42d3b2bc7e
	Left key:    cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
	Right key:   8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Session id:  335683f5d6f68c07f403...9ff0ec0666c8aa758e9f
	Session key: b9543925d432aa649f44...dc567363cbf681ba4dec
	X:
		X0: 7980e2bc73fc7770e4bb...95df8ee7896c29c29624
		X1: 473105cba0ddeb665b0f...23dae373472bd11ac353
		X2: 3eb1e777d3219c16bfb4...b6056d94ce47f8d85577
	Coins:
		r0: 40654d6ad9f8fa0e9e88...28498a3717497d50379a
		r1: dcf216a2f003095e2613...76e851e19a0a630239bb
		r2: 5517f02ba5933ae3e4c5...6e65812e47ac554f7375
	Commitments:
		c0: 48295f823c7aba107c87...a3bd748e2b88edd18489|fcc6fa8d8de0a5df95ca...6422c2222d514c65c02a|8b01e37e50889f0596aab0efcdd95309
		c1: fb4ddba67a0e6ef3dc7f...3b6c31d82921765b5b18|47abb0c7edd90f26f67b...be7c5c0eb9c9fc6e7bd8|bd4206864e76acc8485496674b2f90c5
		c2: 084828fdeea4cffa634a...703d96c71fb7193a1509|89d3d7063f6374a761c2...f11b9f458789f0b3410c|00ddcf95551ff54fc1b3693d236e241e
	Master Key:
		k0: b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
		k1: cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
		k2: 8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   1
	Terminated: 1
Party 2
	Public key:  04b9d39a88b2fa2fa9ca...3d1cb561c8e9c59bcb14
	Secret key:  004000008000400000c0...95bc6fb21854991fc9ac
	Left key:    8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Right key:   b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
	Session id:  335683f5d6f68c07f403...9ff0ec0666c8aa758e9f
	Session key: b9543925d432aa649f44...dc567363cbf681ba4dec
	X:
		X0: 7980e2bc73fc7770e4bb...95df8ee7896c29c29624
		X1: 473105cba0ddeb665b0f...23dae373472bd11ac353
		X2: 3eb1e777d3219c16bfb4...b6056d94ce47f8d85577
	Coins:
		r0: 40654d6ad9f8fa0e9e88...28498a3717497d50379a
		r1: dcf216a2f003095e2613...76e851e19a0a630239bb
		r2: 5517f02ba5933ae3e4c5...6e65812e47ac554f7375
	Commitments:
		c0: 48295f823c7aba107c87...a3bd748e2b88edd18489|fcc6fa8d8de0a5df95ca...6422c2222d514c65c02a|8b01e37e50889f0596aab0efcdd95309
		c1: fb4ddba67a0e6ef3dc7f...3b6c31d82921765b5b18|47abb0c7edd90f26f67b...be7c5c0eb9c9fc6e7bd8|bd4206864e76acc8485496674b2f90c5
		c2: 084828fdeea4cffa634a...703d96c71fb7193a1509|89d3d7063f6374a761c2...f11b9f458789f0b3410c|00ddcf95551ff54fc1b3693d236e241e
	Master Key:
		k0: b5f41f44aefa5eed657b...a43dc21c3f5600b4ada1
		k1: cc74fdf8dd06299d81c0...31e24cfbb63a29763b85
		k2: 8b45f8337ddbc2fbdacf...1238af88f111f86cf8d6
	Pids:
		pid0: Party 0
		pid1: Party 1
		pid2: Party 2
	Accepted:   1
	Terminated: 1
All keys are equal!
Session key: b9543925d432aa649f4429019cf85f6f8708523f2c7adc567363cbf681ba4dec
Session id:  335683f5d6f68c07f403d6ea1ed0100098412165653a9ff0ec0666c8aa758e9f


Time stats
	Init time      : 0.001s (21.72%)
	Round 1-2 time : 0.002s (42.25%)
	Round 3 time   : 0.001s (16.60%)
	Round 4 time   : 0.001s (19.43%)
	Total time     : 0.005s (100.00%)

References

[1] Escribano Pablos, J.I.; González Vasco, M.I.; Marriaga, M.E.; Pérez del Pozo, Á.L. "Compiled Constructions towards Post-Quantum Group Key Exchange: A Design from Kyber," 2020 Mathematics, 8, 1853, doi:10.3390/math8101853

[2] Fujioka, A.; Suzuki, K.; Xagawa K.; Yoneyama K.; "Practical and post-quantum authenticated key exchange from one-way secure key encapsulation mechanism," 2013. In Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security (ASIA CCS '13). Association for Computing Machinery, New York, NY, USA, 83–94. doi:10.1145/2484313.2484323