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Biennial Symposium on Communications

Looping for Encryption Key Generation Over the Internet: A New Frontier in Physical Layer Security

Amir Keyvan Khandani

Published Jul 4, 2023• 1 citation
Publisher

Abstract

Current key sharing techniques rely on the hardness of solving a solvable, but complex, mathematical problem. This entails, in Information Theoretical sense, the encryption key is not secret, it can be found by solving the underlying mathemat-ical problem. Sensitive data we encrypt today using traditional techniques can be recorded by malicious parties and be deciphered in the future whenever improved hacking techniques and supporting computing technology permit. Information Theory proves the existence of methods for sharing of encryption keys that are unconditionally secure, but does not show how to bring such theoretical results to practical use. One of the central information theoretical approaches to key sharing is based on exploiting common randomness. This theoretical result states that if two dependent random variables,$A$and B, are available at Alice and Bob, then, by communicating through a public channel between$A$and B, it is possible to securely share a key of size I(A;B). To bridge the gap between theory and practice, one needs a method to generate two sets of dependent random variables, one at Alice‘s side and the other one at the Bob’ side, as well as a method to extract two identical keys from these dependent random variables. This article presents a novel technique to achieve this goal over the Internet. Dependent random variables are generated by measuring packet travel times between Alice and Bob, and error-free key extraction from dependent random variables is realized by using a randomized Low Density Parity Check Code (LDPC). Through looping of packets between Alice and Bob, the mutual information between random variables is increased. Finally, methods are presented to measure the likelihood values required in decoding the underlying LDPC. It is shown that the key rate is approximately equal to$0.5\log_{9}(4L^{2}/(4L-1))\approx 0.5\log_{2}(L)$where$L$is the number of round trips (loops). Test results (based on measurements between distant nodes over the Internet) are presented, demonstrating the feasibility of the proposed technique. The proposed method is implemented entirely in software (through high-level programming, e.g., using C-language, at the application layer). This operation does not require modifying the underlying network.

DOI
10.1109/bsc57238.2023.10201818

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Current key sharing techniques rely on the hardness of solving a solvable, but complex, mathematical problem. This entails, in Information Theoretical sense, the encryption key is not secret, it can be found by solving the underlying mathemat-ical problem. Sensitive data we encrypt today using traditional techniques can be recorded by malicious parties and be deciphered in the future whenever improved hacking techniques and supporting computing technology permit. Information Theory proves the existence of methods for sharing of encryption keys that are unconditionally secure, but does not show how to bring such theoretical results to practical use. One of the central information theoretical approaches to key sharing is based on exploiting common randomness. This theoretical result states that if two dependent random variables,AAAand B, are available at Alice and Bob, then, by communicating through a public channel betweenAAAand B, it is possible to securely share a key of size I(A;B). To bridge the gap between theory and practice, one needs a method to generate two sets of dependent random variables, one at Alice‘s side and the other one at the Bob’ side, as well as a method to extract two identical keys from these dependent random variables. This article presents a novel technique to achieve this goal over the Internet. Dependent random variables are generated by measuring packet travel times between Alice and Bob, and error-free key extraction from dependent random variables is realized by using a randomized Low Density Parity Check Code (LDPC). Through looping of packets between Alice and Bob, the mutual information between random variables is increased. Finally, methods are presented to measure the likelihood values required in decoding the underlying LDPC. It is shown that the key rate is approximately equal to0.5log⁡9(4L2/(4L−1))≈0.5log⁡2(L)0.5\log_{9}(4L^{2}/(4L-1))\approx 0.5\log_{2}(L)0.5log9​(4L2/(4L−1))≈0.5log2​(L)whereLLLis the number of round trips (loops). Test results (based on measurements between distant nodes over the Internet) are presented, demonstrating the feasibility of the proposed technique. The proposed method is implemented entirely in software (through high-level programming, e.g., using C-language, at the application layer). This operation does not require modifying the underlying network.
This article bridges the gap between two topics used in sharing an encryption key: (i) Key Consolidation, i.e., extracting two identical strings of bits from two information sources with similarities (common randomness). (ii) Quantum-safe Key Encapsulation by incorporating randomness in Public/Private Key pairs. In the context of Key Consolidation, the proposed scheme adds to the complexity Eve faces in extracting useful data from leaked information. In this context, it is applied to the method proposed in [1] for establishing common randomness from round-trip travel times in a packet data network. The proposed method allows adapting the secrecy level to the amount of similarity in common randomness. It can even encapsulate a Quantum-safe encryption key in the extreme case that no common randomness is available. In the latter case, it is shown that the proposed scheme offers improvements with respect to the McEliece cryptosystem which currently forms the foundation for Quantum safe key encapsulation. [1] A. K. Khandani, "Looping for Encryption Key Generation Over the Internet: A New Frontier in Physical Layer Security," 2023 Biennial Symposium on Communications (BSC), Montreal, QC, Canada, 2023, pp. 59-64
Two legitimate parties, referred to as Alice and Bob, wish to generate secret keys from the wireless channel in the presence of an eavesdropper, referred to as Eve, in order to use such keys for encryption and decryption. In general, the secret key rate highly depends on the coherence time of the channel. In particular, a straightforward method of generating secret keys in static environments results in ultra-low rates. In order to resolve this problem, we introduce a low-complexity method called induced randomness. In this method, Alice and Bob independently generate local randomness to be used together with the uniqueness of the wireless channel coefficients in order to enable high-rate secret key generation. In this work, two scenarios are considered: first, when Alice and Bob share a direct communication channel, and second, when Alice and Bob do not have a direct link and communicate through an untrusted relay. After exchanging the induced randomness, post-processing is done by Alice and Bob to generate highly-correlated samples that are used for the key generation. Such samples are then converted into bits, disparities between the sequences generated by Alice and Bob are mitigated, and the resulting sequences are then hashed to compensate for the information leakage to the eavesdropper and to allow consistency checking of the generated key bit sequences. We utilize semantic security measures and information-theoretic inequalities to upper bound the probability of successful eavesdropping attack in terms of the mutual information measures that can be numerically computed. Given certain reasonable system parameters this bound is numerically evaluated to be 2-31and 2-10.57in the first and the second scenario, respectively.
The use of wireless networks for communication has grown significantly in recent times, and continues to develop further. The broadcast nature of wireless communications makes them susceptible to a wide variety of security attacks. Unlike traditional solutions, which usually handle security at the application layer, the primary concern of this dissertation is to analyse and develop solutions for secure communication using channel coding techniques at the physical-layer. \nThe topic of physical layer authenticated encryption using high rate key generation through shared randomness is investigated in this work. First, a physical layer secret key generation scheme is discussed exploiting channel reciprocity in wireless systems. In order to address the susceptibility of this family of schemes to active attacks, a novel physical layer authentication encryption protocol is presented along with its extension to multi-node networks in the presence of active adversaries. Unlike previous work in the area of generating secret keys through shared randomness, it is demonstrated that the proposed scheme is semantically secure with respect to chosen plaintext and chosen cipher text attacks. \nSecondly, in order to increase the rate in bits per seconds at which agreed cryptographic keys are been generated, a multi-level quantization algorithm with public feedback is discussed. It is demonstrated that the proposed scheme is superior to direct information distillation approaches and can substantially increase the key generation rates even at low and medium SNRs. Furthermore, the employment of this low-overhead feedback at the information distillation process can largely simplify the information reconciliation process. \nThe proposed secret key generation schemes are tested for randomness such as required for cryptographic keys. The validation test is perfomed with the aid of National Institute of Standards and Technology (NIST) statistical test suite. The P-values obtained in each of the test carried out indicates that the key sequence generated by our algorithm is random.
Although one-time pad encrypted files can be sent through Internet channels, the need for renewing shared secret keys have made this method unpractical. This work presents a scheme to turn practical the fast sharing of random keys over arbitrary Internet channels. Starting with a shared secret key sequence of length K_0 the users end up with a secure new sequence K >> K_0. Using these sequences for posteriori message encryption the legitimate users have absolute security control without the need for third parties. Additionally, the security level does not depend on the unproven difficulty of factoring numbers in primes. In the proposed scheme a fast optical random source generates random bits and noise for key renewals. The transmitted signals are recorded signals that carries both the random binary signals to be exchanged and physical noise that cannot be eliminated by the attacker. These signals allow amplification over the Internet network without degrading security. The proposed system is also secure against a-posteriori known-plaintext attack on the key. Information-theoretic analysis is presented and bounds for secure operation are quantitatively determined.
Information-theoretically secure communications are possible when channel noise is usable and when the channel has an intrinsic characteristic that a legitimate receiver (Bob) can use the noise more advantageously than an eavesdropper (Eve). This report deals with the case in which the channel does not have such an intrinsic characteristic. Here, we use a pre-shared common key as a tool that extrinsically makes Bob more advantageous than Eve. This method uses error-correcting code in addition to the common key and noise, and manages the three components in random-number transmission. Secret keys are generated from noise, and messages are encrypted with the secret keys in a one-time pad manner. As a result, information leaks meaningful to Eve are restricted to the parity-check symbols for the random numbers. It is possible to derive the candidates of the common key from the parity check symbols, and the security of this method is quantified in terms of the amount of computations needed for an exhaustive search of the candidates, where we evaluate the security by assuming that all parity check symbols leak to Eve without bit errors. Noise contributes to not only generating secret keys but also enhancing the security because the candidates of the common key increase with it.
A hybrid encryption scheme consists of a public-key part called the key encapsulation mechanism (KEM), that is used to generate and establish a shared secret key between two parties, and a (symmetric) secret-key part called the data encapsulation mechanism (DEM) that encrypts the data using the shared key. Hybrid encryption schemes are widely used for securing Internet communication. In this paper, we initiate the study of hybrid encryption in preprocessing model which assumes access to initial correlated variables by all parties (including the eavesdropper), and define information-theoretic KEM (iKEM) that together with a (computationally) secure DEM, results in a hybrid encryption scheme in preprocessing model. We define security of each building block, and prove a composition theorem that guarantees (computational) q-chosen-plaintext attack (CPA) security of the hybrid encryption system if the iKEM and the DEM satisfy q-chosen-encapsulation attack security and one-time security, respectively. We show that an iKEM can be realized by an information-theoretic one-way secret key agreement (OW-SKA) protocol where a single message is transmitted from Alice to Bob, with a new security definition that allowsqqqqueries to Alice. Using a OW-SKA that satisfies this new definition of security, effectively allows the established secret key to be used with a onetime symmetric key encryption system that can be implemented, for example, by XORing the output of a (computationally) secure pseudorandom generator with the message, to provide secure encryption ofqqqarbitrary messages (polynomially bounded length). We discuss our results and directions for future work.