4 research outputs found
Π’Π΅ΠΎΡΠ΅ΡΠΈΠΊΠΎ-ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ Π²ΠΈΡΡΡΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΡΠ΅ΡΠ΅Π²ΠΎΠ³ΠΎ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅ΡΠ΅Ρ Π²Π°ΡΠ°
The most difficult task of secure telecommunication systems using symmetric encryption, due to the need for preliminary and resource-intensive organization of secret channels for delivering keys to network correspondents, is key management. An alternative is the generating keys methods through open communication channels. In information theory, it is shown that these methods are implemented under the condition that the channel information rate of correspondents exceeds the rate of the intruder interception channel. The search for methods that provide the informational advantage of correspondents is being updated. The goal is to determine the information-theoretical conditions for the formation of a virtual network and an interception channel, for which the best ratio of information speeds for correspondents is provided compared to the ratio of the original network and interception channel. The paper proposes an information transfer model that includes a connectivity model and an information transfer method for asymptotic lengths of code words. The model includes three correspondents and is characterized by the introduction of an ideal broadcast channel in addition to an errored broadcast channel. The model introduces a source of "noisy" information, which is transmitted over the channel with errors, so the transmission of code words using the known method of random coding is carried out over the channel without errors. For asymptotic lengths of code words, all actions of correspondents in processing and transmitting information in the model are reduced to the proposed method of transmitting information. The use of the method by correspondents within the framework of the transmission model makes it possible to simultaneously form for them a new virtual broadcast channel with information rate as in the original channel with errors, and for the intruder a new virtual broadcast interception channel with a rate lower than the information rate of the initial interception channel. The information-theoretic conditions for deterioration of the interception channel are proved in the statement. The practical significance of the results obtained lies in the possibility of using the latter to assess the information efficiency of open network key formation in the proposed information transfer model, as well as in the development of well-known scientific achievements of open key agreement. The proposed transmission model can be useful for researching key management systems and protecting information transmitted over open channels. Further research is related to the information-theoretic assessment of the network key throughput, which is the potential information-theoretic speed of network key formation.Π‘Π»ΠΎΠΆΠ½Π΅ΠΉΡΠ΅ΠΉ Π·Π°Π΄Π°ΡΠ΅ΠΉ Π·Π°ΡΠΈΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π»Π΅ΠΊΠΎΠΌΠΌΡΠ½ΠΈΠΊΠ°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ, ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΠΈΡ
ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΠ΅ ΡΠΈΡΡΠΎΠ²Π°Π½ΠΈΠ΅, Π² ΡΠ²ΡΠ·ΠΈ Ρ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡΡ ΠΏΡΠ΅Π΄Π²Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΈ ΡΠ΅ΡΡΡΡΠΎΠ΅ΠΌΠΊΠΎΠΉ ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΈ ΡΠ΅ΠΊΡΠ΅ΡΠ½ΡΡ
ΠΊΠ°Π½Π°Π»ΠΎΠ² Π΄ΠΎΡΡΠ°Π²ΠΊΠΈ ΠΊΠ»ΡΡΠ΅ΠΉ ΡΠ΅ΡΠ΅Π²ΡΠΌ ΠΊΠΎΡΡΠ΅ΡΠΏΠΎΠ½Π΄Π΅Π½ΡΠ°ΠΌ, ΡΠ²Π»ΡΠ΅ΡΡΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΊΠ»ΡΡΠ°ΠΌΠΈ. ΠΠ»ΡΡΠ΅ΡΠ½Π°ΡΠΈΠ²ΠΎΠΉ Π²ΡΡΡΡΠΏΠ°ΡΡ ΠΌΠ΅ΡΠΎΠ΄Ρ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΊΠ»ΡΡΠ΅ΠΉ ΠΏΠΎ ΠΎΡΠΊΡΡΡΡΠΌ ΠΊΠ°Π½Π°Π»Π°ΠΌ ΡΠ²ΡΠ·ΠΈ. Π ΡΠ΅ΠΎΡΠΈΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΡΠΈ ΠΌΠ΅ΡΠΎΠ΄Ρ ΡΠ΅Π°Π»ΠΈΠ·ΡΡΡΡΡ ΠΏΡΠΈ ΡΡΠ»ΠΎΠ²ΠΈΠΈ ΠΏΡΠ΅Π²ΡΡΠ΅Π½ΠΈΡ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΊΠ°Π½Π°Π»Π° ΠΊΠΎΡΡΠ΅ΡΠΏΠΎΠ½Π΄Π΅Π½ΡΠΎΠ² Π½Π°Π΄ ΡΠΊΠΎΡΠΎΡΡΡΡ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅ΡΠ΅Ρ
Π²Π°ΡΠ° Π½Π°ΡΡΡΠΈΡΠ΅Π»Ρ. ΠΠΊΡΡΠ°Π»ΠΈΠ·ΠΈΡΡΠ΅ΡΡΡ ΠΏΠΎΠΈΡΠΊ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ², ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°ΡΡΠΈΡ
ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΠ΅ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΏΡΠ΅ΠΈΠΌΡΡΠ΅ΡΡΠ²Π° ΠΊΠΎΡΡΠ΅ΡΠΏΠΎΠ½Π΄Π΅Π½ΡΠΎΠ². Π¦Π΅Π»Ρ Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π² ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠΈ ΡΠ΅ΠΎΡΠ΅ΡΠΈΠΊΠΎ-ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π²ΠΈΡΡΡΠ°Π»ΡΠ½ΡΡ
ΡΠ΅ΡΠΈ ΠΈ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅ΡΠ΅Ρ
Π²Π°ΡΠ°, Π΄Π»Ρ ΠΊΠΎΡΠΎΡΡΡ
ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°Π΅ΡΡΡ Π»ΡΡΡΠ΅Π΅ Ρ ΠΊΠΎΡΡΠ΅ΡΠΏΠΎΠ½Π΄Π΅Π½ΡΠΎΠ² ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΠΊΠΎΡΠΎΡΡΠ΅ΠΉ ΠΏΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Ρ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ΠΌ ΠΈΡΡ
ΠΎΠ΄Π½ΡΡ
ΡΠ΅ΡΠΈ ΠΈ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅ΡΠ΅Ρ
Π²Π°ΡΠ°. Π ΡΠ°Π±ΠΎΡΠ΅ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ, Π²ΠΊΠ»ΡΡΠ°ΡΡΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ²ΡΠ·Π½ΠΎΡΡΠΈ ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π΄Π»Ρ Π°ΡΠΈΠΌΠΏΡΠΎΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π΄Π»ΠΈΠ½ ΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΡΠ»ΠΎΠ². ΠΠΎΠ΄Π΅Π»Ρ Π²ΠΊΠ»ΡΡΠ°Π΅Ρ ΡΡΠ΅Ρ
ΠΊΠΎΡΡΠ΅ΡΠΏΠΎΠ½Π΄Π΅Π½ΡΠΎΠ² ΠΈ ΠΎΡΠ»ΠΈΡΠ°Π΅ΡΡΡ Π²Π²Π΅Π΄Π΅Π½ΠΈΠ΅ΠΌ ΠΈΠ΄Π΅Π°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΈΡΠΎΠΊΠΎΠ²Π΅ΡΠ°ΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΠΊΠ°Π½Π°Π»Π° Π² Π΄ΠΎΠΏΠΎΠ»Π½Π΅Π½ΠΈΠ΅ ΠΊ ΡΠΈΡΠΎΠΊΠΎΠ²Π΅ΡΠ°ΡΠ΅Π»ΡΠ½ΠΎΠΌΡ ΠΊΠ°Π½Π°Π»Ρ Ρ ΠΎΡΠΈΠ±ΠΊΠ°ΠΌΠΈ. Π ΠΌΠΎΠ΄Π΅Π»ΠΈ Π²Π²Π΅Π΄Π΅Π½ ΠΈΡΡΠΎΡΠ½ΠΈΠΊ Β«Π·Π°ΡΡΠΌΠ»ΡΡΡΠ΅ΠΉΒ» ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΏΠ΅ΡΠ΅Π΄Π°Π΅ΡΡΡ ΠΏΠΎ ΠΊΠ°Π½Π°Π»Ρ Ρ ΠΎΡΠΈΠ±ΠΊΠ°ΠΌΠΈ, ΠΏΠΎΡΡΠΎΠΌΡ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠ° ΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΡΠ»ΠΎΠ² Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΈΠ·Π²Π΅ΡΡΠ½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΡΠ»ΡΡΠ°ΠΉΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΡΡ ΠΏΠΎ ΠΊΠ°Π½Π°Π»Ρ Π±Π΅Π· ΠΎΡΠΈΠ±ΠΎΠΊ. ΠΠ»Ρ Π°ΡΠΈΠΌΠΏΡΠΎΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π΄Π»ΠΈΠ½ ΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΡΠ»ΠΎΠ² Π²ΡΠ΅ Π΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΊΠΎΡΡΠ΅ΡΠΏΠΎΠ½Π΄Π΅Π½ΡΠΎΠ² ΠΏΠΎ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠ΅ ΠΈ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠ΅ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π² ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ²Π΅Π΄Π΅Π½Ρ Π² ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ. ΠΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΊΠΎΡΡΠ΅ΡΠΏΠΎΠ½Π΄Π΅Π½ΡΠ°ΠΌΠΈ Π² ΡΠ°ΠΌΠΊΠ°Ρ
ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΎΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎ ΡΡΠΎΡΠΌΠΈΡΠΎΠ²Π°ΡΡ Π΄Π»Ρ Π½ΠΈΡ
Π½ΠΎΠ²ΡΠΉ Π²ΠΈΡΡΡΠ°Π»ΡΠ½ΡΠΉ ΡΠΈΡΠΎΠΊΠΎΠ²Π΅ΡΠ°ΡΠ΅Π»ΡΠ½ΡΠΉ ΠΊΠ°Π½Π°Π» Ρ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΡΠΊΠΎΡΠΎΡΡΡΡ, ΠΊΠ°ΠΊ ΠΈ Π² ΠΏΠ΅ΡΠ²ΠΎΠ½Π°ΡΠ°Π»ΡΠ½ΠΎΠΌ ΠΊΠ°Π½Π°Π»Π΅ Ρ ΠΎΡΠΈΠ±ΠΊΠ°ΠΌΠΈ, Π° Π΄Π»Ρ Π½Π°ΡΡΡΠΈΡΠ΅Π»Ρ Π½ΠΎΠ²ΡΠΉ Π²ΠΈΡΡΡΠ°Π»ΡΠ½ΡΠΉ ΡΠΈΡΠΎΠΊΠΎΠ²Π΅ΡΠ°ΡΠ΅Π»ΡΠ½ΡΠΉ ΠΊΠ°Π½Π°Π» ΠΏΠ΅ΡΠ΅Ρ
Π²Π°ΡΠ° ΡΠΎ ΡΠΊΠΎΡΠΎΡΡΡΡ ΠΌΠ΅Π½ΡΡΠ΅ΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΏΠ΅ΡΠ²ΠΎΠ½Π°ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅ΡΠ΅Ρ
Π²Π°ΡΠ°. Π’Π΅ΠΎΡΠ΅ΡΠΈΠΊΠΎ-ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΡΡΠ»ΠΎΠ²ΠΈΡ ΡΡ
ΡΠ΄ΡΠ΅Π½ΠΈΡ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅ΡΠ΅Ρ
Π²Π°ΡΠ° Π΄ΠΎΠΊΠ°Π·ΡΠ²Π°Π΅ΡΡΡ Π² ΡΡΠ²Π΅ΡΠΆΠ΄Π΅Π½ΠΈΠΈ. ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ Π·Π½Π°ΡΠΈΠΌΠΎΡΡΡ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π² Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΡΠ»Π΅Π΄Π½ΠΈΡ
Π΄Π»Ρ ΠΎΡΠ΅Π½ΠΊΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΎΡΠΊΡΡΡΠΎΠ³ΠΎ ΡΠ΅ΡΠ΅Π²ΠΎΠ³ΠΎ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΊΠ»ΡΡΠ΅ΠΉ Π² ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ, Π° ΡΠ°ΠΊΠΆΠ΅ Π² ΡΠ°Π·Π²ΠΈΡΠΈΠΈ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
Π½Π°ΡΡΠ½ΡΡ
Π΄ΠΎΡΡΠΈΠΆΠ΅Π½ΠΈΠΉ ΠΎΡΠΊΡΡΡΠΎΠ³ΠΎ ΠΊΠ»ΡΡΠ΅Π²ΠΎΠ³ΠΎ ΡΠΎΠ³Π»Π°ΡΠΎΠ²Π°Π½ΠΈΡ. ΠΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΠΏΠΎΠ»Π΅Π·Π½ΠΎΠΉ Π΄Π»Ρ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΡΠΈΡΡΠ΅ΠΌ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΊΠ»ΡΡΠ°ΠΌΠΈ ΠΈ Π·Π°ΡΠΈΡΡ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ, ΠΏΠ΅ΡΠ΅Π΄Π°Π²Π°Π΅ΠΌΠΎΠΉ ΠΏΠΎ ΠΎΡΠΊΡΡΡΡΠΌ ΠΊΠ°Π½Π°Π»Π°ΠΌ. ΠΠ°Π»ΡΠ½Π΅ΠΉΡΠΈΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ²ΡΠ·Π°Π½Ρ Ρ ΡΠ΅ΠΎΡΠ΅ΡΠΈΠΊΠΎ-ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΠΎΡΠ΅Π½ΠΊΠΎΠΉ ΡΠ΅ΡΠ΅Π²ΠΎΠΉ ΠΊΠ»ΡΡΠ΅Π²ΠΎΠΉ ΠΏΡΠΎΠΏΡΡΠΊΠ½ΠΎΠΉ ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡΠΈ, ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡΠ΅ΠΉ ΡΠΎΠ±ΠΎΠΉ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ ΡΠ΅ΠΎΡΠ΅ΡΠΈΠΊΠΎ-ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ ΡΠΊΠΎΡΠΎΡΡΡ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΠ΅Π²ΠΎΠ³ΠΎ ΠΊΠ»ΡΡΠ°
Secret key generation from Gaussian sources using lattice-based extractors
We propose a lattice-based scheme for secret key generation from Gaussian sources in the presence of an eavesdropper, and show that it achieves the strong secret key capacity in the case of degraded source models, as well as the optimal secret key / public communication rate trade-off. The key ingredients of our scheme are a lattice extractor to extract the channel intrinsic randomness, based on the notion of flatness factor, together with a randomized lattice quantization technique to quantize the continuous source. Compared to previous works, we introduce two new notions of flatness factor based on distance and KL divergence, respectively, which are of independent interest. We prove the existence of secrecy-good lattices under distance and KL divergence, whose and KL flatness factors vanish for volume-to-noise ratios up to . This improves upon the volume-to-noise ratio threshold of the flatness factor