iiap.sci.amiiap.sci.am/pdf/narek_pahlevanyan.pdf · 9 𝑁 𝑁 𝑁 㑅 㑆 𝑁 ̂ 𝑁 ̂ 㑅 㑆 㑅 㑆 㑅 ̂㑆 10 A. Juels and M. Wattenberg, "A fuzzy commitment scheme,"

3

1

3

4

4

6

5

𝐸 → 0,

7

6

𝐸

Հ

7

𝐸

𝐸

8

9

9

𝑋𝑁

𝑆 𝑋𝑁

𝑋𝑁 𝑀

𝑓(𝑆) 𝐼𝐷 𝑀

𝑌𝑁 �̂� 𝑌𝑁 𝑀

�̂�

𝑓(𝑆)

𝑓(𝑆) 𝑓(�̂�)

10 A. Juels and M. Wattenberg, "A fuzzy commitment scheme," in Proc. 6th ACM Conf. Computer and Comm. Security, pp. 28-36, 1999.

10

𝑆 𝐶

𝑓(𝑆) 𝑀 𝐶 𝑋𝑁

𝑌𝑁 𝐶′ = 𝑌𝑁 + 𝑀 = 𝑌𝑁 + 𝑋𝑁 + 𝐶 = 𝐶 + 𝐸𝑣 = 𝑌𝑁 + 𝑋𝑁:

𝐶′ �̂�

�̂� = 𝑆

𝑓(�̂�) 𝑓(𝑆)

𝑆

𝑋𝑁

𝑌𝑁 𝑁

𝑀 �̂�

11

Pr{𝑆 ≠ �̂�} ≈ 0

1

𝑁𝐻(𝑆) ≈

1

𝑁log2|𝑆|

1

𝑁𝐻(𝑆)

1

𝑁𝐼(𝑆 ∧ 𝑀) ≈ 0

1

𝑁𝐼(𝑋𝑁 ∧ 𝑀)

𝑀

𝑋𝑁 𝑌𝑁 𝐼(𝑋𝑁 ∧ 𝑌𝑁)

{𝑄(𝑥, 𝑦), 𝑥 ∈ 𝒳, 𝑦 ∈ 𝒴} բաշխումով

𝒳 𝐱 ≡ 𝑥𝑁 = (𝓍1, 𝓍2, … , 𝓍𝑁)

𝑁 𝒴

𝐲 ≡ 𝑦𝑁 = (𝓎1, 𝓎2, … , 𝓎𝑁)

𝑁

𝑋𝑁 𝑌𝑁

𝑌𝑁

𝑋𝑁

𝑄(𝑥, 𝑦) = 𝑄1(𝑥)𝑄2(𝑦|𝑥), 𝑥 ∈ 𝒳, 𝑦 ∈ 𝒴 :

𝑄𝑁(x, y) = ∏ 𝑄(𝑥𝑛, 𝑦𝑛)

𝑁

𝑛=1

:

𝑋𝑁

𝑆 ∈ {1,2, … , |𝒮|} 𝑀 ∈

{1,2, … , |ℳ|}

𝑓(𝑋𝑁) = (𝑆, 𝑀),

𝑓(∙)

𝑌𝑁 𝑆 �̂�

𝑀

12

𝑔(𝑌𝑁 , 𝑀) = �̂�,

𝑔(∙, ∙)

�̂� 𝑆

𝑅 𝑅 ≥ 0

𝛿 > 0 𝑁

Pr{𝑆 ≠ �̂�} ≤ 𝛿, 1

𝑁𝐻(𝑆) + 𝛿 ≥

1

𝑁log2|𝑆| ≥ 𝑅 − 𝛿,

1

𝑁𝐼(𝑆 ∧ 𝑀) ≤ 𝛿:

𝐼(𝑋 ∧ 𝑌)

𝐸 −

𝐸 → 0

𝑅(𝐸) 𝑅(𝐸) ≥ 0

𝐸 − 𝛿 > 0, 𝐸 > 0 𝑁

Pr{𝑆 ≠ �̂�} ≤ 2−𝑁(𝐸−𝛿)

1

𝑁𝐻(𝑆) + 𝛿 ≥

1

𝑁𝑙𝑜𝑔2|𝑆| ≥ 𝑅(𝐸) − 𝛿,

1

𝑁𝐼(𝑆 ∧ 𝑀) ≤ 𝛿.

𝑄1 = {𝑄1(𝑥), 𝑥 ∈ 𝒳}, 𝑄2 = {𝑄2(𝑦|𝑥), 𝑦 ∈ 𝒴, 𝑥 ∈ 𝒳},𝑃1 = {𝑃1(𝑥), 𝑥 ∈ 𝒳}, 𝑃2 = {𝑃2(𝑦|𝑥), 𝑦 ∈ 𝒴, 𝑥 ∈ 𝒳},

𝑄 = {𝑄(𝑥, 𝑦), 𝑥 ∈ 𝒳, 𝑦 ∈ 𝒴},𝑃 = {𝑃(𝑥, 𝑦), 𝑥 ∈ 𝒳, 𝑦 ∈ 𝒴}.

𝐸 −

13

𝑅(𝐸)

𝑹𝒓(𝑬) = 𝐦𝐢𝐧𝑷:𝑫(𝑷||𝑸)≤𝑬

|𝑰𝑷(𝑿 ∧ 𝒀) + 𝑫(𝑷||𝑸) − 𝑬|+

𝑹𝒔𝒑(𝑬) = 𝐦𝐢𝐧𝑷:𝑫(𝑷||𝑸)≤𝑬

𝑰𝑷(𝑿 ∧ 𝒀):

𝐸 → 0,

lim𝐸→0

𝑅𝑟(𝐸) = lim𝐸→0

𝑅𝑠𝑝(𝐸) = 𝐼𝑄(𝑋 ∧ 𝑌):

𝐸 −

1

𝑁𝐼𝑄1

(𝑀 ∧ 𝑋𝑁) = max𝑃:𝐷(𝑃||𝑄)≤𝐸

(𝐻𝑃(𝑋|𝑌) + 𝐷(𝑃||𝑄) − 𝐸):

14

11

12

15

𝐸

𝐸 −

𝐸 −

𝐸 → 0

1. M. Haroutunian, N. Pahlevanyan, “Information theoretical analysis of biometric secret

key sharing model,” Transactions of IIAP of NAS of RA, Mathematical Problems of

Computer Science, vol. 42, pp. 17-27, 2014.

2. M. Haroutunian, N. Pahlevanyan, “Technical aspects of biometric secret sharing

system construction,” Scientific Proceedings of GSPI, Vol. A, Number 1, pp. 116-121,

2014.

3. Н. Пайлеванян “Технологические решения вычислений теоретико-

информационных результатов в коммуникационных системах,” Международная

научно-техническая конференция студентов и молодых специалистов из стран-

16

участниц РСС по направлениям «Информационные технологии и системы связи»,

Сборник тезисов, стр. 96-99, Москва, 2015.

4. M. Haroutunian, N. Pahlevanyan, “Experimentation of Advanced Inftheo module for

R on the example of biometric generated secret key sharing system,” International

Journal “Information Content and Processing”, Vol. 2, Number 1, pp. 62-70, 2015.

5. N. Pahlevanyan, M. Haroutunian, “Technical solutions of developing Advanced

Inftheo new module for R,” Proceedings of the 10th International Conference on

Computer Science and Information Technologies, Yerevan, Armenia, pp. 306-309,

2015.

6. N. Pahlevanyan, M. Haroutunian, “Results of performance analysis of Advanced

Inftheo new package for R,” Transactions of IIAP of NAS of RA, Mathematical

Problems of Computer Science, vol. 45, pp. 5-13, 2016.

17

18

𝐸 → 0

𝐸 → 0

19

The relevance of the research.

The aim of the research.

Scientific novelty of the research.

𝐸

𝐸 → 0

20

Practical significance of the research:

Results of the research.

𝐸

𝐸 𝐸 → 0