j1u.netlify.com

• Attacks on A5/1 as used in GSM. In 2003, Barkan et al. Published several attacks on GSM encryption. The first is an active attack. GSM phones can be convinced to use the much weaker A5/2 cipher briefly. A5/2 can be broken easily, and the phone uses the same key as for the stronger A5/1 algorithm.
• Kc key generation. The Kc key is generated at both the MS and the AuC by applying the cipher key-generation algorithm (A8) to RAND (generated by the AuC) and Ki—unique to each MS. Kc key generated at the AuC is passed to the MSC/VLR along with RAND and SRES as part of each triplet. 3: Encryption process in GSM.
• How Do Authentication and Key generation work in a GSM network? Encryption in the GSM network utilizes a Challenge/Response mechanism. The Mobile Station (MS) signs into the network.
• We would capture gsm data in wireshark through osmocom-bb and analyse how the entire process of gsm authentication and encryption happens. We will also see how the location update process happens. In GSM, KASUMI is used in the A5/3 key stream generator and in GPRS in the GEA3 key stream generator. Generation of encryption key(Kc).

1. Gsm Key Generation And Encryption Processor
2. Gsm Key Generation And Encryption Process Examples
3. Gsm Key Generation And Encryption Process Free

How Authentication Center (AUC) works in GSM, imsi and creation of sim card, algorithms defined on allocation of imsi, authentication process, subscriber. Using Kc, A5 and the GSM hyperframe number, encryption between the MS and the BSS can now occur over the air interface. Ki = Authentication key, assigned at random together with.

• Cryptography Tutorial

• Cryptography Useful Resources

• Selected Reading

Public Key Cryptography

Unlike symmetric key cryptography, we do not find historical use of public-key cryptography. It is a relatively new concept.

Symmetric cryptography was well suited for organizations such as governments, military, and big financial corporations were involved in the classified communication.

With the spread of more unsecure computer networks in last few decades, a genuine need was felt to use cryptography at larger scale. The symmetric key was found to be non-practical due to challenges it faced for key management. This gave rise to the public key cryptosystems.

The process of encryption and decryption is depicted in the following illustration −

The most important properties of public key encryption scheme are −

• Different keys are used for encryption and decryption. This is a property which set this scheme different than symmetric encryption scheme.

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• Each receiver possesses a unique decryption key, generally referred to as his private key.

• Receiver needs to publish an encryption key, referred to as his public key.

• Some assurance of the authenticity of a public key is needed in this scheme to avoid spoofing by adversary as the receiver. Generally, this type of cryptosystem involves trusted third party which certifies that a particular public key belongs to a specific person or entity only.

• Encryption algorithm is complex enough to prohibit attacker from deducing the plaintext from the ciphertext and the encryption (public) key.

• Though private and public keys are related mathematically, it is not be feasible to calculate the private key from the public key. In fact, intelligent part of any public-key cryptosystem is in designing a relationship between two keys.

There are three types of Public Key Encryption schemes. We discuss them in following sections −

RSA Cryptosystem

This cryptosystem is one the initial system. It remains most employed cryptosystem even today. The system was invented by three scholars Ron Rivest, Adi Shamir, and Len Adleman and hence, it is termed as RSA cryptosystem.

We will see two aspects of the RSA cryptosystem, firstly generation of key pair and secondly encryption-decryption algorithms.

Generation of RSA Key Pair

Gsm Key Generation And Encryption Processor

Each person or a party who desires to participate in communication using encryption needs to generate a pair of keys, namely public key and private key. The process followed in the generation of keys is described below −

• Generate the RSA modulus (n)

  • Select two large primes, p and q.

  • Calculate n=p*q. For strong unbreakable encryption, let n be a large number, typically a minimum of 512 bits.

• Find Derived Number (e)

  • Number e must be greater than 1 and less than (p − 1)(q − 1).

  • There must be no common factor for e and (p − 1)(q − 1) except for 1. In other words two numbers e and (p – 1)(q – 1) are coprime.

• Form the public key

  • The pair of numbers (n, e) form the RSA public key and is made public.

  • Interestingly, though n is part of the public key, difficulty in factorizing a large prime number ensures that attacker cannot find in finite time the two primes (p & q) used to obtain n. This is strength of RSA.

• Generate the private key

  • Private Key d is calculated from p, q, and e. For given n and e, there is unique number d.

  • Number d is the inverse of e modulo (p - 1)(q – 1). This means that d is the number less than (p - 1)(q - 1) such that when multiplied by e, it is equal to 1 modulo (p - 1)(q - 1).

  • This relationship is written mathematically as follows −

The Extended Euclidean Algorithm takes p, q, and e as input and gives d as output.

Example

An example of generating RSA Key pair is given below. (For ease of understanding, the primes p & q taken here are small values. Practically, these values are very high).

• Let two primes be p = 7 and q = 13. Thus, modulus n = pq = 7 x 13 = 91.

• Select e = 5, which is a valid choice since there is no number that is common factor of 5 and (p − 1)(q − 1) = 6 × 12 = 72, except for 1.

• The pair of numbers (n, e) = (91, 5) forms the public key and can be made available to anyone whom we wish to be able to send us encrypted messages.

• Input p = 7, q = 13, and e = 5 to the Extended Euclidean Algorithm. The output will be d = 29.

• Check that the d calculated is correct by computing −

• Hence, public key is (91, 5) and private keys is (91, 29).

Encryption and Decryption

Once the key pair has been generated, the process of encryption and decryption are relatively straightforward and computationally easy.

Interestingly, RSA does not directly operate on strings of bits as in case of symmetric key encryption. It operates on numbers modulo n. Hence, it is necessary to represent the plaintext as a series of numbers less than n.

RSA Encryption

• Suppose the sender wish to send some text message to someone whose public key is (n, e).

• The sender then represents the plaintext as a series of numbers less than n.

• To encrypt the first plaintext P, which is a number modulo n. The encryption process is simple mathematical step as −

• In other words, the ciphertext C is equal to the plaintext P multiplied by itself e times and then reduced modulo n. This means that C is also a number less than n.

• Returning to our Key Generation example with plaintext P = 10, we get ciphertext C −

RSA Decryption

• The decryption process for RSA is also very straightforward. Suppose that the receiver of public-key pair (n, e) has received a ciphertext C.

• Receiver raises C to the power of his private key d. The result modulo n will be the plaintext P.

• Returning again to our numerical example, the ciphertext C = 82 would get decrypted to number 10 using private key 29 −

RSA Analysis

The security of RSA depends on the strengths of two separate functions. The RSA cryptosystem is most popular public-key cryptosystem strength of which is based on the practical difficulty of factoring the very large numbers.

• Encryption Function − It is considered as a one-way function of converting plaintext into ciphertext and it can be reversed only with the knowledge of private key d.

• Key Generation − The difficulty of determining a private key from an RSA public key is equivalent to factoring the modulus n. An attacker thus cannot use knowledge of an RSA public key to determine an RSA private key unless he can factor n. It is also a one way function, going from p & q values to modulus n is easy but reverse is not possible.

If either of these two functions are proved non one-way, then RSA will be broken. In fact, if a technique for factoring efficiently is developed then RSA will no longer be safe.

The strength of RSA encryption drastically goes down against attacks if the number p and q are not large primes and/ or chosen public key e is a small number.

ElGamal Cryptosystem

Along with RSA, there are other public-key cryptosystems proposed. Many of them are based on different versions of the Discrete Logarithm Problem.

ElGamal cryptosystem, called Elliptic Curve Variant, is based on the Discrete Logarithm Problem. It derives the strength from the assumption that the discrete logarithms cannot be found in practical time frame for a given number, while the inverse operation of the power can be computed efficiently.

Let us go through a simple version of ElGamal that works with numbers modulo p. In the case of elliptic curve variants, it is based on quite different number systems.

Generation of ElGamal Key Pair

Each user of ElGamal cryptosystem generates the key pair through as follows −

• Choosing a large prime p. Generally a prime number of 1024 to 2048 bits length is chosen.

• Choosing a generator element g.

  • This number must be between 1 and p − 1, but cannot be any number.

  • It is a generator of the multiplicative group of integers modulo p. This means for every integer m co-prime to p, there is an integer k such that g^k=a mod n.

    For example, 3 is generator of group 5 (Z₅ = {1, 2, 3, 4}).

• Choosing the private key. The private key x is any number bigger than 1 and smaller than p−1.

• Computing part of the public key. The value y is computed from the parameters p, g and the private key x as follows −

• Obtaining Public key. The ElGamal public key consists of the three parameters (p, g, y).

  For example, suppose that p = 17 and that g = 6 (It can be confirmed that 6 is a generator of group Z₁₇). The private key x can be any number bigger than 1 and smaller than 71, so we choose x = 5. The value y is then computed as follows −

• Thus the private key is 62 and the public key is (17, 6, 7).

Encryption and Decryption

The generation of an ElGamal key pair is comparatively simpler than the equivalent process for RSA. But the encryption and decryption are slightly more complex than RSA.

ElGamal Encryption

Suppose sender wishes to send a plaintext to someone whose ElGamal public key is (p, g, y), then −

• Sender represents the plaintext as a series of numbers modulo p.

• To encrypt the first plaintext P, which is represented as a number modulo p. The encryption process to obtain the ciphertext C is as follows −

  • Randomly generate a number k;
  • Compute two values C1 and C2, where −

• Send the ciphertext C, consisting of the two separate values (C1, C2), sent together.

• Referring to our ElGamal key generation example given above, the plaintext P = 13 is encrypted as follows −

  • Randomly generate a number, say k = 10
  • Compute the two values C1 and C2, where −

• Send the ciphertext C = (C1, C2) = (15, 9).

ElGamal Decryption

• To decrypt the ciphertext (C1, C2) using private key x, the following two steps are taken −

  • Compute the modular inverse of (C1)^x modulo p, which is (C1)^-x , generally referred to as decryption factor.

  • Obtain the plaintext by using the following formula −

• In our example, to decrypt the ciphertext C = (C1, C2) = (15, 9) using private key x = 5, the decryption factor is

• Extract plaintext P = (9 × 9) mod 17 = 13.

ElGamal Analysis

In ElGamal system, each user has a private key x. and has three components of public key − prime modulus p, generator g, and public Y = g^x mod p. The strength of the ElGamal is based on the difficulty of discrete logarithm problem.

The secure key size is generally > 1024 bits. Today even 2048 bits long key are used. On the processing speed front, Elgamal is quite slow, it is used mainly for key authentication protocols. Due to higher processing efficiency, Elliptic Curve variants of ElGamal are becoming increasingly popular.

Elliptic Curve Cryptography (ECC)

Elliptic Curve Cryptography (ECC) is a term used to describe a suite of cryptographic tools and protocols whose security is based on special versions of the discrete logarithm problem. It does not use numbers modulo p.

ECC is based on sets of numbers that are associated with mathematical objects called elliptic curves. There are rules for adding and computing multiples of these numbers, just as there are for numbers modulo p.

ECC includes a variants of many cryptographic schemes that were initially designed for modular numbers such as ElGamal encryption and Digital Signature Algorithm.

It is believed that the discrete logarithm problem is much harder when applied to points on an elliptic curve. This prompts switching from numbers modulo p to points on an elliptic curve. Also an equivalent security level can be obtained with shorter keys if we use elliptic curve-based variants.

The shorter keys result in two benefits −

• Ease of key management
• Efficient computation

These benefits make elliptic-curve-based variants of encryption scheme highly attractive for application where computing resources are constrained.

RSA and ElGamal Schemes – A Comparison

Let us briefly compare the RSA and ElGamal schemes on the various aspects.

End-to-end encryption (E2EE) is a system of communication where only the communicating users can read the messages. In principle, it prevents potential eavesdroppers – including telecom providers, Internet providers, and even the provider of the communication service – from being able to access the cryptographic keys needed to decrypt the conversation.^[1]

In many messaging systems, including email and many chat networks, messages pass through intermediaries and are stored by a third party, from which they are retrieved by the recipient. Even if the messages are encrypted, they are typically only encrypted 'in transit', and are stored in decrypted form by the third party. This allows the third party to provide search and other features, or to scan for illegal and unacceptable content, but also means they can be read and misused by anyone who has access to the stored messages on the third party system, whether this is by design or via a backdoor. This can be seen as a concern in many cases where privacy is very important, such as persons living under repressive governments, whistleblowing, mass surveillance, businesses whose reputation depends on its ability to protect third party data, negotiations and communications that are important enough to have a risk of targeted 'hacking', and where sensitive subjects such as health, and information about minors are involved.

End-to-end encryption is intended to prevent data being read or secretly modified, other than by the true sender and recipient(s). The messages are encrypted by the sender but the third party does not have a means to decrypt them, and stores them encrypted. The recipient retrieves the encrypted data and decrypts it themselves.

Because no third parties can decipher the data being communicated or stored, for example, companies that use end-to-end encryption are unable to hand over texts of their customers' messages to the authorities.^[2]

Key exchange[edit]

In an E2EE system, encryption keys must only be known to the communicating parties. To achieve this goal, E2EE systems can encrypt data using a pre-arranged string of symbols, called a pre-shared secret (PGP), or a one-time secret derived from such a pre-shared secret (DUKPT). They can also negotiate a secret key on the spot using Diffie-Hellman key exchange (OTR).^[3]

Modern usage[edit]

As of 2016, typical server-based communications systems do not include end-to-end encryption. These systems can only guarantee the protection of communications between clients and servers, meaning that users have to trust the third parties who are running the servers with the original texts. End-to-end encryption is regarded as safer because it reduces the number of parties who might be able to interfere or break the encryption.^[4] In the case of instant messaging, users may use a third-party client to implement an end-to-end encryption scheme over an otherwise non-E2EE protocol.^[5]

Some non-E2EE systems, such as Lavabit and Hushmail, have described themselves as offering 'end-to-end' encryption when they did not.^[6] Other systems, such as Telegram and Google Allo, have been criticized for not having end-to-end encryption, which they offer, enabled by default. Telegram did not enable end-to-end encryption by default on VoIP calls while users were using desktop software version, but that problem was fixed quickly.^[7][8]

Some encrypted backup and file sharing services provide client-side encryption. The encryption they offer is here not referred to as end-to-end encryption, because the services are not meant for sharing messages between users. However, the term 'end-to-end encryption' is often used as a synonym for client-side encryption.^{[citation needed]}

The term 'end-to-end encryption' originally only meant that the communication is never decrypted during its transport from the sender to the receiver.^[9]For example, around 2003, E2EE has been proposed as an additional layer of encryption for GSM^[10] or TETRA^[11], in addition to the existing radio encryption protecting the communication between the mobile device and the network infrastructure. This has been standardised by SFPG for TETRA^[12]. Note that in TETRA E2EE, the keys are generated by a Key Management Centre (KMC) or a Key Management Facility (KMF), not by the communicating users.^[13]

Later, around 2014, the meaning of 'end-to-end encryption' started to evolve, requiring that not only the communication stays encrypted during transport, but also that the provider of the communication service is not able to decrypt the communications. This new meaning is now the widely accepted one.

Challenges[edit]

Man-in-the-middle attacks[edit]

End-to-end encryption ensures that data is transferred securely between endpoints. But, rather than try to break the encryption, an eavesdropper may impersonate a message recipient (during key exchange or by substituting his public key for the recipient's), so that messages are encrypted with a key known to the attacker. After decrypting the message, the snoop can then encrypt it with a key that they share with the actual recipient, or their public key in case of asymmetric systems, and send the message on again to avoid detection. This is known as a man-in-the-middle attack (MITM).^[1][14]

Authentication[edit]

Most end-to-end encryption protocols include some form of endpoint authentication specifically to prevent MITM attacks. For example, one could rely on certification authorities or a web of trust.^[15] An alternative technique is to generate cryptographic hashes (fingerprints) based on the communicating users’ public keys or shared secret keys. The parties compare their fingerprints using an outside (out-of-band) communication channel that guarantees integrity and authenticity of communication (but not necessarily secrecy), before starting their conversation. If the fingerprints match, there is in theory, no man in the middle.^[1]

When displayed for human inspection, fingerprints are usually encoded into hexadecimal strings. These strings are then formatted into groups of characters for readability. For example, a 128-bit MD5 fingerprint would be displayed as follows:

Some protocols display natural language representations of the hexadecimal blocks.^[16] As the approach consists of a one-to-one mapping between fingerprint blocks and words, there is no loss in entropy. The protocol may choose to display words in the user's native (system) language.^[16] This can, however, make cross-language comparisons prone to errors.^[17] In order to improve localization, some protocols have chosen to display fingerprints as base 10 strings instead of hexadecimal or natural language strings.^[18][17] Modern messaging applications can also display fingerprints as QR codes that users can scan off each other's devices.^[18]

Endpoint security[edit]

The end-to-end encryption paradigm does not directly address risks at the communications endpoints themselves. Each user's computer can still be hacked to steal his or her cryptographic key (to create a MITM attack) or simply read the recipients’ decrypted messages both in real time and from log files. Even the most perfectly encrypted communication pipe is only as secure as the mailbox on the other end.^[1] Major attempts to increase endpoint security have been to isolate key generation, storage and cryptographic operations to a smart card such as Google's Project Vault.^[19] However, since plaintext input and output are still visible to the host system, malware can monitor conversations in real time. A more robust approach is to isolate all sensitive data to a fully air gapped computer.^[20] PGP has been recommended by experts for this purpose:

Gsm Key Generation And Encryption Process Examples

If I really had to trust my life to a piece of software, I would probably use something much less flashy — GnuPG, maybe, running on an isolated computer locked in a basement.

Gsm Key Generation And Encryption Process Free

However, as Bruce Schneier points out, Stuxnet developed by US and Israel successfully jumped air gap and reached Natanz nuclear plant's network in Iran.^[21] To deal with key exfiltration with malware, one approach is to split the Trusted Computing Base behind two unidirectionally connected computers that prevent either insertion of malware, or exfiltration of sensitive data with inserted malware.^[22]

Backdoors[edit]

A backdoor is usually a secret method of bypassing normal authentication or encryption in a computer system, a product, or an embedded device, etc.^[23] Companies may also willingly or unwillingly introduce backdoors to their software that help subvert key negotiation or bypass encryption altogether. In 2013, information leaked by Edward Snowden showed that Skype had a backdoor which allowed Microsoft to hand over their users' messages to the NSA despite the fact that those messages were officially end-to-end encrypted.^[24][25]

See also[edit]

• Comparison of instant messaging clients#Secure messengers – a table overview of instant messaging clients that offer end-to-end encryption
• Comparison of VoIP software#Secure VoIP software – a table overview of VoIP clients that offer end-to-end encryption
• Client-side encryption – the encryption of data before it is transmitted to a server

References[edit]

1. ^ ^abcd'Hacker Lexicon: What Is End-to-End Encryption?'. WIRED. 2014-11-25. Archived from the original on 23 December 2015. Retrieved 22 December 2015.
2. ^McLaughlin, Jenna (21 December 2015). 'Democratic Debate Spawns Fantasy Talk on Encryption'. The Intercept. Archived from the original on 23 December 2015.
3. ^Chris Alexander, Ian Avrum Goldberg (February 2007). Improved User Authentication in Off-The-Record Messaging(PDF). Proceedings of the 2007 ACM Workshop on Privacy in Electronic Society. pp. 41–47. doi:10.1145/1314333.1314340. ISBN9781595938831. Archived(PDF) from the original on 2016-02-27.
4. ^'End-to-End Encryption'. EFF Surveillance Self-Defense Guide. Electronic Frontier Foundation. Archived from the original on 5 March 2016. Retrieved 2 February 2016.
5. ^'How to: Use OTR for Windows'. EEF Surveillance Self-Defence Guide. Electronic Frontier Foundation. Archived from the original on 20 January 2016. Retrieved 2 February 2016.
6. ^Grauer, Yael. 'Mr. Robot Uses ProtonMail, But It Still Isn't Fully Secure'. WIRED. Archived from the original on 2017-03-09.
7. ^'Why Telegram's security flaws may put Iran's journalists at risk'. Committee to Protect Journalists. 31 May 2016. Archived from the original on 19 August 2016. Retrieved 23 September 2016.
8. ^Hackett, Robert (21 May 2016). 'Here's Why Privacy Savants Are Blasting Google Allo'. Fortune. Time Inc. Archived from the original on 10 September 2016. Retrieved 23 September 2016.
9. ^Baran, Paul (1964). 'IX. Security, Secrecy, and Tamper-Free Considerations. III. Some Fundamentals of Cryptography'. On Distributed Communications. RAND corporation.
10. ^Moldal, L.; Jorgensen, T. (11 February 2003). End to end encryption in GSM, DECT and satellite networks using NSK200. IET.
11. ^Murgatroyd, Brian (11 February 2003). End to end encryption in public safety TETRA networks. IET.
12. ^'New chair for the SFPG'. 2007.
13. ^Morquecho Martinez, Raul Alejandro (31 March 2016). Delivery of encryption keys in TETRA networks(PDF) (Master's Thesis). Aalto University.
14. ^Schneier, Bruce; Ferguson, Niels; Kohno, Tadayoshi (2010). Cryptography engineering : design principles and practical applications. Indianapolis, IN: Wiley Pub., inc. p. 183. ISBN978-0470474242.
15. ^'What is man-in-the-middle attack (MitM)? - Definition from WhatIs.com'. IoT Agenda. Archived from the original on 5 January 2016. Retrieved 7 January 2016.
16. ^ ^ab'pEp White Paper'(PDF). pEp Foundation Council. 18 July 2016. Archived(PDF) from the original on 1 October 2016. Retrieved 11 October 2016.
17. ^ ^abMarlinspike, Moxie (5 April 2016). 'WhatsApp's Signal Protocol integration is now complete'. Open Whisper Systems. Archived from the original on 10 October 2016. Retrieved 11 October 2016.
18. ^ ^abBudington, Bill (7 April 2016). 'WhatsApp Rolls Out End-To-End Encryption to its Over One Billion Users'. Deeplinks Blog. Electronic Frontier Foundation. Archived from the original on 12 September 2016. Retrieved 11 October 2016.
19. ^Julie Bort, Matt Weinberger 'Google's Project Vault is a tiny computer for sending secret messages'Archived 2017-08-08 at the Wayback Machine, Business Insider, NYC May 29, 2015
20. ^Whonix Wiki 'Air Gapped OpenPGP Key'Archived 2017-08-08 at the Wayback Machine
21. ^Bruce Schneier 'Air Gaps'Archived 2017-06-09 at the Wayback Machine, Schneier on Security, October 11, 2013
22. ^'maqp/tfc'. GitHub. Archived from the original on 31 March 2017. Retrieved 26 April 2018.
23. ^Eckersley, Peter; Portnoy, Erica (8 May 2017). 'Intel's Management Engine is a security hazard, and users need a way to disable it'. www.eff.org. Archived from the original on 6 March 2018. Retrieved 7 March 2018.
24. ^Goodin, Dan (20 May 2013). 'Think your Skype messages get end-to-end encryption? Think again'. Ars Technica. Archived from the original on 22 December 2015.
25. ^Greenwald, Glenn; MacAskill, Ewen; Poitras, Laura; Ackerman, Spencer; Rushe, Dominic (12 July 2013). 'Microsoft handed the NSA access to encrypted messages'. the Guardian. Archived from the original on 19 November 2015.

Further reading[edit]

• Ermoshina, Ksenia; Musiani, Francesca; Halpin, Harry (September 2016). 'End-to-End Encrypted Messaging Protocols: An Overview'(PDF). In Bagnoli, Franco; et al. (eds.). Internet Science. INSCI 2016. Florence, Italy: Springer. pp. 244–254. doi:10.1007/978-3-319-45982-0_22. ISBN978-3-319-45982-0.