Stream Cipher the Operation of the Keystream Generator in A5/1, A
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Stream Cipher The operation of the keystream generator in A5/1, a LFSR-based stream cipher used to encrypt mobile phone conversations. In cryptography, a stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher each plaintext digit is encrypted one at a time with the corresponding digit of the keystream, to give a digit of the cyphertext stream. An alternative name is a state cipher , as the encryption of each digit is dependent on the current state. In practice, a digit is typically a bit and the combining operation an exclusive-or (xor). The pseudorandom keystream is typically generated serially from a random seed value using digital shift registers. The seed value serves as the cryptographic key for decrypting the ciphertext stream. Stream ciphers represent a different approach to symmetric encryption from block ciphers. Block ciphers operate on large blocks of digits with a fixed, unvarying transformation. This distinction is not always clear-cut: in some modes of operation, a block cipher primitive is used in such a way that it acts effectively as a stream cipher. Stream ciphers typically execute at a higher speed than block ciphers and have lower hardware complexity. However, stream ciphers can be susceptible to serious security problems if used incorrectly: see stream cipher attacks — in particular, the same starting state (seed) must never be used twice. Loose inspiration from the one-time pad Stream ciphers can be viewed as approximating the action of a proven unbreakable cipher, the one-time pad (OTP), sometimes known as the Vernam cipher. A one-time pad uses a keystream of completely random digits. The keystream is combined with the plaintext digits one at a time to form the ciphertext. This system was proved to be secure by Claude Shannon in 1949. However, the keystream must be (at least) the same length as the plaintext, and generated completely at random. This makes the system very cumbersome to implement in practice, and as a result the one-time pad has not been widely used, except for the most critical applications. A stream cipher makes use of a much smaller and more convenient key — 128 bits, for example. Based on this key, it generates a pseudorandom keystream which can be combined with the plaintext digits in a similar fashion to the one-time pad. However, this comes at a cost: because the keystream is now pseudorandom, and not truly random, the proof of security associated with the one-time pad no longer holds: it is quite possible for a stream cipher to be completely insecure. Types of stream ciphers A stream cipher generates successive elements of the keystream based on an internal state. This state is updated in essentially two ways: if the state changes independently of the plaintext or ciphertext messages, the cipher is classified as a synchronous stream cipher. By contrast, self- synchronising stream ciphers update their state based on previous ciphertext digits. Synchronous stream ciphers In a synchronous stream cipher a stream of pseudo-random digits is generated independently of the plaintext and ciphertext messages, and then combined with the plaintext (to encrypt) or the ciphertext (to decrypt). In the most common form, binary digits are used (bits), and the keystream is combined with the plaintext using the exclusive or operation (XOR). This is termed a binary additive stream cipher . In a synchronous stream cipher, the sender and receiver must be exactly in step for decryption to be successful. If digits are added or removed from the message during transmission, synchronisation is lost. To restore synchronisation, various offsets can be tried systematically to obtain the correct decryption. Another approach is to tag the ciphertext with markers at regular points in the output. If, however, a digit is corrupted in transmission, rather than added or lost, only a single digit in the plaintext is affected and the error does not propagate to other parts of the message. This property is useful when the transmission error rate is high; however, it makes it less likely the error would be detected without further mechanisms. Moreover, because of this property, synchronous stream ciphers are very susceptible to active attacks — if an attacker can change a digit in the ciphertext, he might be able to make predictable changes to the corresponding plaintext bit; for example, flipping a bit in the ciphertext causes the same bit to be flipped in the plaintext. Self-synchronizing stream ciphers Another approach uses several of the previous N ciphertext digits to compute the keystream. Such schemes are known as self-synchronizing stream ciphers , asynchronous stream ciphers or ciphertext autokey (CTAK) . The idea of self-synchronization was patented in 1946, and has the advantage that the receiver will automatically synchronise with the keystream generator after receiving N ciphertext digits, making it easier to recover if digits are dropped or added to the message stream. Single-digit errors are limited in their effect, affecting only up to N plaintext digits. An example of a self-synchronising stream cipher is a block cipher in cipher feedback (CFB) mode. Linear feedback shift register-based stream ciphers Binary stream ciphers are often constructed using linear feedback shift registers (LFSRs) because they can be easily implemented in hardware and can be readily analysed mathematically. The use of LFSRs on their own, however, is insufficient to provide good security. Various schemes have been proposed to increase the security of LFSRs. Non-linear combining functions One approach is to use n LFSRs in parallel, their outputs combined using an n-input binary Boolean function ( F). Because LFSRs are inherently linear, one technique for removing the linearity is to feed the outputs of several parallel LFSRs into a non-linear Boolean function to form a combination generator . Various properties of such a combining function are critical for ensuring the security of the resultant scheme, for example, in order to avoid correlation attacks. Clock-controlled generators Normally LFSRs are stepped regularly. One approach to introducing non-linearity is to have the LFSR clocked irregularly, controlled by the output of a second LFSR. Such generators include the stop-and-go generator, the alternating step generator and the shrinking generator. An alternating step generator comprises three linear feedback shift registers, which we will call LFSR0, LFSR1 and LFSR2 for convenience. The output of one of the registers decides which of the other two is to be used; for instance if LFSR2 outputs a 0, LFSR0 is clocked, and if it outputs a 1, LFSR1 is clocked instead. The output is the exclusive OR of the last bit produced by LFSR0 and LFSR1. The initial state of the three LFSRs is the key. The stop-and-go generator (Beth and Piper, 1984) consists of two LFSRs. One LFSR is clocked if the output of a second is a "1", otherwise it repeats its previous output. This output is then (in some versions) combined with the output of a third LFSR clocked at a regular rate. The shrinking generator takes a different approach. Two LFSRs are used, both clocked regularly. If the output of the first LFSR is "1", the output of the second LFSR becomes the output of the generator. If the first LFSR outputs "0", however, the output of the second is discarded, and no bit is output by the generator. This mechanism suffers from timing attacks on the second generator, since the speed of the output is variable in a manner that depends on the second generator's state. This can be alleviated by buffering the output. Filter generator Another approach to improving the security of an LFSR is to pass the entire state of a single LFSR into a non-linear filtering function . Other designs RC4 is one of the most widely used stream cipher designs. Instead of a linear driving device, one may use a nonlinear update function. For example, Klimov and Shamir proposed triangular functions (T-Functions) with a single cycle on n bit words. Security For a stream cipher to be secure, its keystream must have a large period and it must be impossible to recover the cipher's key or internal state from the keystream. Cryptographers also demand that the keystream be free of even subtle biases that would let attackers distinguish a stream from random noise, and free of detectable relationships between keystreams that correspond to related keys or related cryptographic nonces. This should be true for all keys (there should be no weak keys ), and true even if the attacker can know or choose some plaintext or ciphertext . As with other attacks in cryptography, stream cipher attacks can be certificational , meaning they aren't necessarily practical ways to break the cipher but indicate that the cipher might have other weaknesses. Securely using a secure synchronous stream cipher requires that one never reuse the same keystream twice; that generally means a different nonce or key must be supplied to each invocation of the cipher. Application designers must also recognize that most stream ciphers don't provide authenticity , only privacy : encrypted messages may still have been modified in transit. Short periods for stream ciphers have been a practical concern. For example, 64-bit block ciphers like DES can be used to generate a keystream in output feedback (OFB) mode. However, when not using full feedback, the resulting stream has a period of around 2 32 blocks on average; for many applications, this period is far too low. For example, if encryption is being performed at a rate of 8 megabytes per second, a stream of period 2 32 blocks will repeat after about a half an hour.