GRID computing includes applications, some of which are intelligence sensitive (genetics, space, industrial intellectual property, etc) and need to remain confidential. Current security is mostly based based on public (asymmetric) key algorithms (Salomaa, 1996) – hash function algorithms easy to calculate in direct, but estimated as impossible in reverse. The base assumption to this assertion is the difficulty of factorising prime numbers. This received however a serious blow in 1994 (Shor, 1994), when it was shown that (a hypothetical future) quantum computer could rapidly factorise prime numbers via a polynomial algorithm. As such messages could be intercepted and stored today awaiting for the availability of quantum processors, when they could conceivably be deciphered. Evidently, data with short “life-span” (2-5 years) is perfectly safe today, however censi, geological data, etc have long-term implications and need to be adequately protected. The other main security contender currently in use is the symmetric-key AES encryption (Daemen and Rijmen, 1996-2001 and 2006), that comes in 3 versions of key length 128, 192 and 256 bit (with 10, 12, and 14 rounds, respectively). For AES-128 there is no known attack faster than the 2128 complexity of exhaustive search. However, AES-192 and AES-256 were recently shown (Biryukov and Khovratovich, 2009) to be breakable by attacks of 2176 and 2119 complexities. While these are much faster than the exhaustive search, they are non-practical, and do not to pose a real threat (at the rate the world produces today data, ca. 0.2⋅1021 bytes/year (261 × 256-bit ciphertexts) it would take 258 ≅ 1017 years data’s worth to recover just one AES key). The US National Security Agency (Hathaway, 2003) stated that “The design and strength of all key lengths of the AES algorithm (i.e., 128, 192 and 256) are sufficient to protect classified information up to the secret level.” From this assessment and the simple estimates above, it is apparent that given adequate key distribution protection AES cannot be broken – at least not in the next 1017 years (for 1 key). The secret key carrier on the other hand needs to be a stable long-term committed technology, that would not come under question any time soon (including from futuristic quantum processor attacks).
GRID computing includes applications, some of which are intelligence sensitive (genetics, space, industrial intellectual property, etc) and need to remain confidential. Current security is mostly based based on public (asymmetric) key algorithms (Salomaa, 1996) – hash function algorithms easy to calculate in direct, but estimated as impossible in reverse. The base assumption to this assertion is the difficulty of factorising prime numbers. This received however a serious blow in 1994 (Shor, 1994), when it was shown that (a hypothetical future) quantum computer could rapidly factorise prime numbers via a polynomial algorithm. As such messages could be intercepted and stored today awaiting for the availability of quantum processors, when they could conceivably be deciphered. Evidently, data with short “life-span” (2-5 years) is perfectly safe today, however censi, geological data, etc have long-term implications and need to be adequately protected. The other main security contender currently in use is the symmetric-key AES encryption (Daemen and Rijmen, 1996-2001 and 2006), that comes in 3 versions of key length 128, 192 and 256 bit (with 10, 12, and 14 rounds, respectively). For AES-128 there is no known attack faster than the 2128 complexity of exhaustive search. However, AES-192 and AES-256 were recently shown (Biryukov and Khovratovich, 2009) to be breakable by attacks of 2176 and 2119 complexities. While these are much faster than the exhaustive search, they are non-practical, and do not to pose a real threat (at the rate the world produces today data, ca. 0.2⋅1021 bytes/year (261 × 256-bit ciphertexts) it would take 258 ≅ 1017 years data’s worth to recover just one AES key). The US National Security Agency (Hathaway, 2003) stated that “The design and strength of all key lengths of the AES algorithm (i.e., 128, 192 and 256) are sufficient to protect classified information up to the secret level.” From this assessment and the simple estimates above, it is apparent that given adequate key distribution protection AES cannot be broken – at least not in the next 1017 years (for 1 key). The secret key carrier on the other hand needs to be a stable long-term committed technology, that would not come under question any time soon (including from futuristic quantum processor attacks).
Motivation The ability to guarantee security and privacy in communication are critical factors in encouraging people to accept and trust new tools and methods for today's information-based society (e.g. in eCommerce or eHealth) and for future services (e.g. eGovernment, eVoting). Cybercrime already hinders these new possibilities by creating widespread mistrust in these new services. Another problem is that a (perhaps unpublicized) break-through in mathematics or computer science could completely compromise current state-of-the-art encryption methods overnight, even those which are the basis of all existing internet banking transactions. This is because the security of cutting-edge public-key cryptography (conventional cryptography) relies on the computational difficulty of certain mathematical tasks, meaning that conventional cryptography alone can neither provide any evidence of eavesdropping nor guarantee strong security. The trend towards faster electronics provides the ability to handle longer keys, thus providing better security, but also increases the possibility to break keys. This also has another worrying effect: even using today's most advanced available security technology to protect data during communication with best practice and without making any mistakes, the ongoing improvements in technology (which hence require longer key lengths to ensure security) mean that today's transmitted data will not be secure for more than a few years. Thus, while encrypted data might be safe today, it can still be stored by the adversary now and then broken later on once the future technology has caught up with today's encryption. Alternatively, modern quantum cryptography has created a new paradigm for cryptographic communication, which provides strong, long-term security and incontrovertible evidence of any attempted eavesdropping which is based on theoretically and experimentally proven laws of nature.
Traditionally, information security needed encryption, authentication, key management, non-repudiation and authorization which were being met using several techniques. Standardization of algorithms by National Institute of Standards and Technology (NIST) has facilitated international communication for banking and information transfer using these standards. Encryption can be carried out using Advanced Encryption Standard (AES) using variable block lengths (128, 192 or 256 bits) and variable key lengths (128, 192 or 256 bits). Solutions for light weight applications such as those for Internet of Things (IoT) are also being standardized. Message integrity is possible using host of hash algorithms such as SHA-1, SHA-2 etc., and more recently using SHA-3 algorithm. Authentication is possible using well known Rivest-Shamir-Adleman (RSA) algorithm needing 2048/4096 bit operations. Elliptic Curve Cryptography (ECC) is also quite popular and used in several practical systems such as WhatsApp, Blackberry etc. Key exchange is possible using Diffie-Hellman algorithm and its variations. Digital Signatures can be carried out using RSA algorithm or Elliptic Curve Digital Signature Algorithm (ECDSA) or DSA (Digital Signature Algorithm). All these algorithms derive security from difficulty in solving some mathematical problems such as factorization problem or discrete logarithm problem. Though published literature gives evidence of solving factorization problem upto 768 bits only, it is believed that using Quantum computers, these problems could be solved by the end of this decade. This is due to availability of the pioneering work of Shor and Grover [1]. For factoring an integer of N bits, Shor’s algorithm takes quantum gates. As such, there is ever growing interest in being ready for the next decade with algorithms that may resist attacks in the quantum computer era. NIST has foreseen this need and has invited proposals from researchers all over the world. In the first round, about 66 submissions were received which have been scrutinized for completeness of submissions , novelty of the approach and security and 25 of these were promote to second round to improve based on the comments received on the first round submission. These will be analyzed for security and some will be selected for final recommendation for use by industry. These are for encryption/decryption, key agreement, hashing and Digital Signatures for both hardware and software implementations. In this paper, we present a brief survey of the state of the art in post-Quantum Cryptography (PQC) followed by study of one of technique referred to as Learning With Errors (LWE) in some detail.
The defense of public key cryptography (PKC) lies in computational issues like the difficulty of factorizing enormous prime numbers and the discrete logarithm calculations. Such kinds of algorithms are called one-way functions because although it is straightforward to compute output given input, it is difficult to compute input if output is given. It is expected that such numerical or computational issues which are utilized in current cryptographic plans are difficult to address for an adversary utilizing present PCs. Yet, many organizations are attempting to assemble a high-powered quantum PC and in the future quantum PCs will be available for business use. Traditional asymmetric cryptographic algorithms are not secure against strong quantum machines. Shor’s algorithm running on a powerful quantum PC is able to solve integer factorization problems and discrete logarithm problems in polynomial time. So, asymmetric algorithms that are used today, like RSA, DSA and Diffie-Hellman will become insecure. Similarly, Grover’s algorithm running on a powerful quantum computer poses a serious threat to symmetric key algorithms which uses small key size. There is a need to work on alternate algorithms to resist quantum threat. NIST has already started with a process for the standardization of algorithms which are known as post-quantum cryptography (PQC) algorithms. Specialists globally are exploring progress toward post-quantum cryptography.
The work is devoted to the study of the problems of using the technology of quantum distribution of secret keys, namely the problems of using and forming new secret keys, based on the generation of quantum keys and the distribution of new keys in networks of complex topologies. In secure communication systems, information is transmitted over public networks, and thus is available to a potential attacker for carrying out various types of attacks. A potential attacker is able to store encrypted data transmitted over network channels, and attempt to decrypt it later, when technical means and attacks on information protection algorithms will allow, in an acceptable time, to carry out decryption. This is the basic principle of "Store now, decrypt later", which is one of the problems of information protection systems. For block ciphers, there is a parameter - the key load, which limits the amount of information that one key can process using the data protection algorithm. NIST recommends a time frame for using secret keys, calculated in years. In the field of information security, there are more significant restrictions on the key load, related to the number of blocks that can be processed by one key, caused by attacks on block ciphers. With these restrictions, there is a need to regularly change the secret key used, and search for options for generating and delivering keys between two network nodes that organize a secure information transmission channel. Changing the secret key to a new key, independent of the previous one, allows you to protect the transfer of confidential information when the key used is compromised. The technology of creating a quantum computer allows you to effectively attack known algorithms for generating secret keys based on the factorization of large numbers or the complexity of calculating a discrete logarithm. The quantum Shor algorithm [5, 6] allows you to solve these problems in polynomial time, so it is necessary to look for alternative solutions to the problem of regular changes in the network channel of the secret key in a pair of nodes. It is important to take into account the need to ensure the quality of Perfect forward secrecy, when the master key is compromised, all subsequent secret keys must not be compromised. To achieve this property of modern encryption algorithms, there is a periodic update of master keys. To prevent the accumulation of information, to successfully carry out attacks by the attacker and to comply with the load requirement on the secret key, it is necessary to solve the problem of regular changes of the secret, and regular generation/delivery of keys to network nodes. Given the urgent needs that are intensively developing today in the secure and high-speed transmission of information, and no less, the rapid growth of technical capabilities, there is a need to develop options in advance that will ensure the security of information during transmission. Regular change, in geographically dispersed data protection systems, of common secret keys, in the case of ensuring the independence of secret keys, allows successfully solving the task.
The practical implementation of quantum information technologies requires, for the most part, highly advanced and currently experimental procedures. One exception is quantum cryptography, or quantum key distribution, which has been successfully demonstrated in many laboratories and has reached an advanced level of development. It will probably become the first commercial application of quantum information. In quantum key distribution, Alice and Bob exploit a quantum channel to create a secret shared key comprising a random string of binary digits. This key can then be used to protect a subsequent communication between them. The principal idea is that the secrecy of the key distribution is ensured by the laws of quantum physics. Proving security for practical communication systems is a challenging problem and requires techniques that are beyond the scope of this book. At a fundamental level, however, the ideas are simple and may readily be understood with the knowledge we have already acquired. Quantum cryptography is the latest idea in the long history of secure (and not so secure) communications and, if it is to develop, it will have to compete with existing technologies. For this reason we begin with a brief survey of the history and current state of the art in secure communications before turning to the possibilities offered by quantum communications. The history of cryptography is a long and fascinating one. As a consequence of the success or, more spectacularly, the failure of ciphers, wars have been fought, battles decided, kingdoms won, and heads lost. In the information age, ciphers and cryptosystems have become part of everyday life; we use them to protect our computers, to shop over the Internet, and to access our money via an ATM (automated teller machine). One of the oldest and simplest of all ciphers is the transposition or Caesarean cipher (attributed to Julius Caesar), in which the letters are shifted by a known (and secret) number of places in the alphabet. If the shift is 1, for example, then A is enciphered as B, B→C, · · ·, Y→Z, Z→A. A shift of five places leads us to make the replacements A→F, B→G, · · ·, Y→D, Z→E.
In today's medical world, Medical Cyber-Physical Systems (MCPS) are becoming more and more important because they allow medical equipment that are linked to receive data, be monitored, and make decisions automatically in real time. However, strong and future-proof security measures are needed because medical data is sensitive and confidential; The Risk of getting exposed online is growing. Traditional cryptographic systems can be broken by attacks that use quantum mechanics and computers that are getting faster. This makes quantum-secured communication very important. By using Quantum Key Distribution (QKD), this study solves the important problem of keeping key management and sharing safe in MCPS. Our goal is to create a safe and effective quantum-enhanced encryption system that protects privacy, stability, and resistance to threats from other parties. The research suggests a mixed cryptography system that combines symmetric keys produced by quantum randomness with RSA-AES encryption methods. This would benefit from both the strengths of quantum randomness and well-known cryptographic standards. Using a seven-step QKD process to make a quantum key: random bit generation, photon state encoding, quantum transfer, basis reconciliation, spying detection, privacy amplification, and symmetric encryption via XOR are the steps that are used. The safe AES-GCM encryption of medical data is reinforced by RSA encryption of AES keys, providing two levels of privacy. Man-in-the-Middle (MITM), Brute-Force, Dictionary, Timing, and Chosen Cipher text Attacks (CCA) are some of the offender models used in the experimental review. Findings show that QKD provides strong protection against key theft and hacking, and the mixed RSA-AES system performs well in terms of encryption time, verification, and decoding accuracy. Attack modelling results show that the system is good at finding or reducing intrusions. The study creates a quantum-secure key sharing system that can be used on a large scale to protect important data in medical cyber-physical settings.