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bkz2.py

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2024-07-31 18:17:20 +02:00

bkz.py

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combinatorials.py

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Readme.md

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sis_parameter_estimation.ipynb

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Readme.md

SIS parameters and attacks

Pre-testnet parameters

These were the original parameters of the original pre-print of Vortex

`log_2(q)`	`log_2(\beta)`	`n`	SVP (L2)	SVP (Loo)	BKZ attack	CPW attack	#limbs	pi
64	5	32	136.12	257.92	135.22	143.0	52	1664
64	7	64	187.51	396.8	160.64	287.07	37	2368
64	11	128	233.94	476.16	151.97	598.14	24	3072
64	16	256	315.41	634.88	158.74	1272.31	16	4096
64	22	512	451.48	952.32	181.86	2741.67	12	6144
64	32	1024	614.42	1269.76	182.46	5967.82	8	8192
254	3	2	66.04	105.4	75.13	192.5	86	172
254	4	4	90.57	158.72	95.7	242.12	64	256
254	5	8	135.24	252.96	134.2	261.1	52	416
254	7	16	186.05	367.04	159.36	270.0	37	592
254	11	32	232.19	476.16	150.7	524.0	24	768
254	16	64	313.07	634.88	157.36	1262.46	16	1024
254	24	128	412.06	872.96	150.29	2720.33	11	1408
254	32	256	609.74	1269.76	180.8	5921.27	8	2048
254	51	512	761.0	1587.2	144.96	13013.81	6	3072

Current parameters

The current parameters that are used in Linea

`log_2(q)`	`log_2(beta)`	`n`	SVP (L2)	SVP (Loo)	BKZ attack	CPW attack	#limbs	pi
64	2	32	315.41	634.88	371.53	144.0	128	4096
64	4	64	315.41	634.88	358.29	305.57	64	4096
64	6	128	415.27	872.96	415.0	598.14	43	5504
64	10	256	494.99	1111.04	380.99	1272.31	26	6656
64	16	512	614.42	1269.76	344.85	2741.67	16	8192
64	22	1024	886.27	1904.64	401.92	5967.82	12	12288
254	1	3	238.9	472.44	281.37	225.25	256	768
254	2	7	275.99	551.18	324.59	259.03	128	896
254	4	16	313.07	634.88	355.56	270.0	64	1024
254	6	32	412.06	853.12	411.68	637.0	43	1376
254	10	64	491.19	1031.68	377.78	1262.46	26	1664
254	16	128	609.74	1269.76	341.83	2720.33	16	2048
254	24	256	807.72	1745.92	333.14	5921.27	11	2816
254	32	512	1203.09	2539.52	405.68	13013.8	8	4096

Future parameters

Parameters that we contemplating for the future

`log_2(q)`	`log_2(beta)`	`n`	SVP (L2)	SVP (Loo)	BKZ attack	CPW attack	#limbs	pi
256	1	2	165.9	317.44	194.27	194.0	256	512
256	2	4	165.9	317.44	193.56	244.0	128	512
256	4	7	147.22	277.76	162.04	261.01	64	448
256	8	18	184.59	357.12	145.31	451.0	32	576
256	16	54	268.69	535.68	131.45	1027.0	16	864
256	24	112	365.34	763.84	130.2	2217.54	11	1232
256	32	192	464.91	952.32	130.64	4107.0	8	1536
64	1	19	371.47	753.92	439.65	129.04	256	4864
64	2	20	203.28	396.8	238.03	129.04	128	2560
64	4	32	165.9	317.44	183.87	143.98	64	2048
64	8	64	165.9	317.44	128.65	287.07	32	2048
64	16	216	268.69	535.68	131.45	1000.43	16	3456
64	24	448	365.34	833.28	130.2	2217.54	11	4928
64	32	768	464.91	952.32	130.64	4107.0	8	6144