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18

Post-quantum security: As you note, quantum attacks are not known to break lattice-based cryptosystems. But some other proposals like McEliece, as well as most symmetric primitives are not known to be poly-time breakable on a quantum computer. Security from worst case assumptions: In security proofs for cryptosystems we typically assume that some problem ...


16

Contrary to the other answer, I'll be assuming the hash function is of the password-oriented kind; and my answer will be: input size has almost no influence on speed in good practice, even for much longer input than in the question. Password-oriented (or entropy-stretching, key-stretching) hash functions are, for example, suitable to transform a (password, ...


16

There are two important differences between AES-128 and AES-256: AES-128 has 10 rounds, AES-256 has 14 The key expansion process (that is, how they generate subkeys) is different If your AES-128 encryption hardware just takes a plaintext block and a 128 bit key, and produces a ciphertext block, well, no, there's not much you can do. In this case, the ...


12

The security level of an elliptic curve group is approximately $\log_2{0.886\sqrt{2^n}}$. You can use this to approximate the security level of a $n$-bit key, eg: $\log_2{0.886\sqrt{2^{571}}} = 285.32537860389294$ The real computation (at least for curves over a finite field defined by a prime $p$) is $ \log_2{\sqrt{\pi/4}\sqrt{ℓ}} $, where $ℓ$ is the ...


11

Bitslicing is a technique where a computation is Reduced to elementary operations (called gates) with two bit inputs (typically NOR, XOR, and similar like OR AND NAND NXOR), rather than operations on words or integers spanning several bits. Executed in parallel, with as many simultaneous instances (on a single CPU) as there are bits in some register kind, ...


9

The fastest block cipher is identity, which leaves input blocks completely unchanged. This is infinitely fast on all platforms; however, it is not secure. So maybe you want the fastest block cipher that still offers some given non-trivial level of security? Then it depends a lot on what you want to implement the block cipher on. With recent PC, you would ...


8

ECDSA should in general create signatures faster than RSA for the same cryptographic strength if you just look at the mathematics. In the end the modular exponentiation is performed for smaller numbers. However, ECDSA depends on a random number generator, so ECDSA speeds may be slower if the random number generator blocks for any reason (and not using a good ...


8

It depends. Specifically, it depends on the type of cipher, and on the way it's used. For stream ciphers like RC4, and for block ciphers like AES in CTR and OFB modes, decryption is effectively identical to encryption, and thus takes the exact same time. (Minor exception: encryption may require generating a unique nonce / IV, which might take a small ...


8

"Cycles" are CPU instruction cycles. Cycles per byte roughly measures how many instructions, in a given instruction set, are needed to produce each byte of output. They're a reasonably-good relative measure of the performance of different algorithms. Generally, when you measure an algorithm's cycles per byte, you use carefully controlled conditions. You ...


8

The basic idea of bitslicing, or SIMD within a register, involves two parts: expressing the cipher in terms of single-bit logical operations (AND, OR, XOR, NOT, etc.), as if you were implementing it in hardware, and carrying out those operations for multiple instances of the cipher in parallel, using bitwise operations on a CPU. That is, in a bitsliced ...


8

It depends how the “AES-128 encryption hardware units” you mention are actually defined. I've already encountered processors that allow to independently compute AES operations such as $\texttt{SubBytes}$ and $\texttt{MixColumns}$ – which are the same regardless the key size involved (128 or 256 bits). In that case: yes, it can speed up the calculation for ...


7

325 MB/s is already good, i.e. you will not get much more with another implementation. Also, SHA-1 is a sequential algorithm, so multiple cores or a GPU will not help you. Specialized hardware is probably your best bet to make SHA-1 faster. (Also, if SHA-1 is the bottleneck then you are able to move data around faster than that, which is impressive; usually,...


7

Yes, AES-128 is intended to be the standard block cipher for building a secure and efficient symmetric cryptosystem using some block cipher operating mode, like CTR for encryption or GCM for authenticated encryption; efficiency can be particularly good when there is hardware support for AES and GCM. There might be better choices in the case at hand, like ...


7

All hashes I know of are block oriented. The time required to calculate the hash scales with the number of blocks to be hashed. There is a small constant overhead dealing with the IV and, possibly, a finalization function.


7

Is Rijndael the fastest block cipher in the world? No. On an Intel 64 Sandy Bridge without AES-NI, AES (a subset of Rijndael) is outperfomed by ChaCha20 (and also likely by Threefish 512 which has about 6-7cpb cost on an older Intel Core 2 Duo with 64-bit ASM (link: original Skein paper PDF)) as opposed to AES' 11 cpb. (7.59 cpb on an Intel Core 2) ...


6

From the diagram on CTR mode you can notice that there are no dependencies between any of the phases of the pipeline. If you have more than one block-size worth of data, you can process each block-size chunk completely independently of the others by calculating $\mathrm{ciphertext}_i = E(\mathrm{key}, \mathrm{nonce} \, || \, \mathrm{counter}_i) \oplus \...


6

In RSA encryption as practiced (that is, to encipher a message which is a short symmetric key), the message size after padding is fixed and equal to the modulus size. Thus the size of the message has no impact on performance. Calculating a modular inverse is performed only during key generation, that is seldom. Also, it has low cost compared to generating ...


6

Computations on elliptic curves are more efficient. Roughly speaking, when the base field has size $n$ (for DH/ElGamal/DSA, the size in bits of the modulus $p$; for elliptic curves, the size of the field for point coordinates) and a "security level" $t$ (e.g. $t = 80$ for "80-bit security" as can be expected when using a 160-bit subgroup and a 160-bit hash ...


6

Given the choice, it is preferable to use the block encryption operation of AES, since it often faster than block decryption (never slower AFAIK). For this reason, AES-CTR is defined to use the block encryption operation of AES exclusively; that's both for AES-CTR encryption and AES-CTR decryption, which are the same operation except for IV generation/input. ...


6

Dedicated stream ciphers typically are, or at least can be, somewhat faster than constructions based on block ciphers. (If they weren't, there would be no point in using them, since a block cipher can do everything a dedicated stream cipher can.) What you gain in speed (and possibly code size), however, you lose in versatility: A block cipher (in CTR / ...


6

The previous answer has the correct formula for estimating the security level of prime field elliptic curves. However, the table seems to just list the closest Koblitz curve sizes used, as Richie Frame points out. If you computed the actual security strength of the curves in question, you would not end up with exactly the values in the left column. For ...


6

If you are using the full HKDF each time, you could possibly save time by only using the Extract portion once and Expand once per derived key. That could even halve the total time taken, if you had a worst case situation. Another speedup possibility within HKDF is to use another hash. Either a faster hash or one that matches the required key length better. ...


5

A "general computer" simply doesn't exist, test for yourself with this command: openssl speed rsa As an example here is the output on a Mac Pro 2007 withIntel Xeon 5130: Doing 512 bit private rsa's for 10s: 67450 512 bit private RSA's in 9.95s Doing 512 bit public rsa's for 10s: 961891 512 bit public RSA's in 9.94s Doing 1024 bit private rsa's for 10s: ...


5

Predicting speed by looking at the assembly is hard, especially since processors do all sorts of tricks which have memory (e.g. branch prediction). So yes, this is all about measuring. There is an art to it; for instance, you would rather repeatedly encrypt the same relatively small buffer (4 or 8 kB) so as to avoid cache effects. One method is to do the ...


5

They measure it. Once upon a time, CPUs were simple enough that you really code compute the amount of time for a stretch of code by looking up the clocks per instruction in the manual, add them all together, and that'd be the total time. However, CPU manufacturers have added more and more optimizations and parallelism; this makes the CPUs run faster (for ...


5

Pretty much all modern encryption systems (including AES, in any standard mode) are data-agnostic: they are designed to encrypt any byte (or bit) stream regardless of its content, and their performance does not depend in any way on what the stream contains. Indeed, if this were not the case, that would open the encryption scheme to timing attacks — if ...


5

Bitslicing is a technique that allows multiple instructions/Data points to be encoded into a single register. The idea is that you encode several bitwise operations within a single register. So, instead of 32 bitwise OR operations in sequence, you could reduce the total number of operations by cramming the data into SIMD registers and executing in ...


5

Rabin-Williams signature verification with 3072 bit keys is much faster than EdDSA signature verification of comparable security (when done in software). How much depends on care of coding, hardware, EdDSA parameters. Two data points: in the eBATS benchmarks for a skylake CPU, ronald3072 signature verification (RSA with $e=3$ as an OpenSSL wrapper, by ...


5

In lattice-based encryption schemes, the encryption is often slower than the decryption (not artificially, but just as the natural way it works). See this paper Efficient Software Implementation of Ring-LWE Encryption (encryption is 3 times slower than decryption).


5

Perhaps not of relevance if the question is meant in a purely thoretical (i.e. asymptotical) sense, but the CBC encryption mode is inherently sequential, while decryption can easily be performed in parallel.



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