When doing the same on .NET 4.52 - I get an RsaCryptoServiceProvider with only 1024 bits keysize. up to 2504). In my mind, until there are proofs that the currently known attacks (GNFS-based attacks) are the best that can be found, or at least some heuristic argument that we can’t do better than the current attacks, the probability for an unknown RSA attack is therefor, as strange as it may sound, 100%. Hungarian / Magyar Russian / Русский While this requires some additional computing power, microprocessors have kept pace with the requirements and there is minimal impact to the entities creating or validating signatures. Some commercial CAs that I have used before restrict the RSA key size to one of 1024, 2048 or 4096 only. ... (RSA… I tried to make the point of using a non-standard key size clear in the post, see especially the wrap-up in the final paragraph. The size of Key Modulus range from 360 to 2048. (Inherited from AsymmetricAlgorithm) : Create() Creates an instance of the default implementation of the RSA algorithm.. It appears there is some remote chance, higher than 0%, that my speculation is true. Strength: 110.11760837749330 As an approximation, consider how many non-negative integers there are that meet these size constraints. $ openssl ecparam -list_curves My blog uses a 2736 bit key size RSA key. This site uses Akismet to reduce spam. The size of the key actually refers to the size (in bits) of the modulus, N, not the size of any of the public or private keys.Two randomly selected primes, p and q, should be chosen such that they are approximately the same length to ensure that any attempts to factor the modulus are much more difficult. The second assumption is that the unknown attack(s) are not as efficient for some key sizes than others. I haven’t seen anyone talk about this, or provide a writeup, that is consistent with my views. Generates a new RSA private key using the provided backend. German / Deutsch How many valid RSA public keys are there are that are exactly N bits in length (that is, bit N-1 is 1 and all bits >= N are 0)? Strength: 112.01273358822347. Is there a difference between a 2000-bit key and a 2048-bit key beginning with 48 zero bits? Today’s recommendations (see keylength.com) suggest that 2048 is on the weak side for long-term keys (5+ years), so there has been a trend to jump to 4096. Chinese Simplified / 简体中文 Slovak / Slovenčina If your threat model includes an organisation which can afford the resources required to crack a ~4000-bit RSA key, then you fighting the wrong battle. So by avoiding values with the high bit set, at best you've doubled the brute-forcer's work. If lets say 3333 is as slow as 4096, 3333 would be a really bad choice. Thai / ภาษาไทย SSH supports several public key algorithms for authentication keys. Back to the speculation that leads me to this choice. RSA with 2048-bit keys. NIST tells us a 2048 bit RSA key is equivalent to a 112 bit symmetric cipher. It seems likely that most attacks in realistic settings will have a huge pre-computation step to speed it up. There are exactly as many N-bit non-negative integers as there are < N-bit integers. Enable JavaScript use, and try again. Romanian / Română This is an interesting topic, even though the article is written in a bit speculative way. Learn how your comment data is processed. “To be fair I should mention that there’s one standard NIST curve using a nice prime, namely 2^521 – 1; but the sheer size of this prime makes it much slower than NIST P-256.”, It’s this one: French / Français Serbian / srpski Croatian / Hrvatski Italian / Italiano You config says you are creating "rss" keys, which is invalid. This is the reason given: "With some suites, the size of the key is the only factor that determines the strength of the key exchange. Here I am making up the 95% number. The input data, clear.txt, has 138 bytes = 1104 bits, which is larger than the RSA key size. Choosing an Algorithm and Key Size. The most common methods are assumed to be weak against sufficiently powerful quantum computers in the future. How many valid RSA public keys are there that are less than N bits in length? It supports key sizes from 384 bits to 512 bits in increments of 8 bits if you have the Microsoft Base Cryptographic Provider installed. $ echo 7295 | ./keysize-NIST.bc I do this when I generate OpenPGP/SSH keys (using GnuPG with a smartcard like this) and PKIX certificates (using GnuTLS or OpenSSL, e.g. It depends. This would allow us to express a 2048 bit RSA key with only 522 bits. I am not a mathematician though. Clear() Releases all resources used by the AsymmetricAlgorithm class. RSA signature verification is the same (very quick), only RSA signature creation is affected, and yes, it will be slower. At the implementation level, it seems reasonable to assume that implementing a RSA cracker for arbitrary key sizes could be more difficult and costlier than focusing on particular key sizes. With better understanding of RSA security levels, the common key size evolved into 768, 1024, and later 2048. Although the RSA certificate is quite safe in the present, companies have already started planning for life after RSA. Then I assume that by avoiding the efficient key sizes I can increase the difficulty to a sufficient level. Probably not by a significant factor, but increasing it a factor of twice or five times as difficult could be worth the small price to pay for using an unusual key size. Strength: 256.00032964845911, $ echo 2048 | ./keysize-NIST.bc But it's not clear to me that this is much of a win. RSA Laboratories has from time to time provided key size recommendations, primarily for the R Eight years ago, in the Summer 1995 issue of CryptoBytes , we recommended a minimum key s for user keys, 1024 bits for enterprise keys and 2048 bits for root keys, a practice that has been It’s likely safe to use. What if using a non-standard key size singles your keys out for special attention? Putting my argument together, I have 1) identified some downsides of using non-standard RSA Key sizes and discussed their costs and implications, and 2) mentioned some speculative upsides of using non-standard key sizes. print “Strength: “, p, “\n”, $ echo 2868 | ./keysize-NIST.bc Because DSA key length is limited to 1024, and RSA key length isn’t limited, so one can generate much stronger RSA keys than DSA keys, I prefer using RSA over DSA. Greek / Ελληνικά These include: rsa - an old algorithm based on the difficulty of factoring large numbers. For something similar to GNFS attacks, I believe the same algorithm applies equally for a RSA key size of 2048, 2730 and 4096 and that the running time depends mostly on the key size. The public key is public after all, and my argument doesn’t involve hiding anything. Vietnamese / Tiếng Việt. Another cost is that RSA signature operations are slowed down. It is not strictly covered by what I wrote, so it really should be part of the argument. There are also post-quantum algorithms, but they are newer and adopting them today requires a careful cost-benefit analysis. Some smart-cards also restrict the key sizes, sadly the YubiKey has this limitation. Hi Jooseppi! For EHSx and BGS5 modules for the RSA key a key size of 2048 is used. It is the largest of the RSA numbers and carried the largest cash prize for its factorization, $200,000. Korean / 한국어 Larger keys provide more security; currently 1024 and below are considered breakable while 2048 or 4096 are reasonable default key sizes for new keys. Do you have any concerns about the quality of implementation in endpoints that support non-PoT key sizes? The fastest way to do it is to have the gmp extension installed and, failing that, the slower bcmath extension. Japanese / 日本語 Indeed, everyone will be able to see what public key size I am using. DISQUS terms of service. A significant burden would be if implementations didn’t allow selecting unusual key sizes. RSA numbers - Wikipedia > RSA-2048 has 617 decimal digits (2,048 bits). All SSL/TLS certificates used today have the key size of 2048-bit, making your website safe. The final assumption is that by using non-standard key sizes I raise the bar sufficiently high to make an attack impossible. I am not aware of any argument that the odds of my speculation is 0% likely to be true. Your blog title is “Why I don’t Use 2048 or 4096 RSA Key Sizes” but your blog uses 2048. Strength: 192.00346260354399 Eventually attacks become public, and then there is a chance that I might be slightly safer because of my approach. 1. RSA Key size selection is the first important decision when selecting RSA for a cryptosystem. The attacks to be worried about are not strictly brute-force attacks, of course, and valid RSA public keys are not evenly distributed across all non-negative integers. Currently, I would guess that more than 95% of all RSA key sizes on the Internet are 1024, 2048 or 4096 though. RSA-krypteringen (Rivest–Shamir–Adleman) är en av de mest kända krypteringsalgoritmerna.Det var den första allmänt beskrivna algoritmen som använder så kallad asymmetrisk kryptering.Detta innebär att man använder en nyckel för att kryptera ett meddelande och en annan för att dekryptera det. If you end up in a fallback path of sorts, I’m fully expecting it to be bitrotted and less audited. Please note that DISQUS operates this forum. Pingback: Why I don’t Use 2048 or 4096 RSA Key Sizes https://blog.josefsson.o… | Dr. Roy Schestowitz (罗伊). This is to understand the cost of the trade-off. A key size of at least 2048 bits is recommended for RSA; 4096 bits is better. I don’t see this as nearly as a big risk for RSA. DJB also mildly likes the NIST P-512 curve. Setting a minimum key size results in a handshake failure when either side's certificate contains an RSA key smaller than the minimum size. In my experience, enough common applications support uncommon key sizes, for example GnuPG, OpenSSL, OpenSSH, FireFox, and Chrome. There is also ECDSA — which has had a comparatively slow uptake, for a number of reasons — that is widely available and is a reasonable choice when Ed25519 is not available. The performance of RSA private-key operations starts to suffer at 4096, and the bandwidth requirements is causing issues in some protocols. To be honest, this scenario appears unlikely. With non-standard key sizes, I mean a RSA key size that is not 2048 or 4096. Choosing modulus greater than 512 will take longer time. 🙁. I have used non-standard RSA key size for maybe 15 years. Slovenian / Slovenščina The size of the resulting product, called the modulus n, is usually expressed in bit length and forms the key size. Deploying this on a large scale may have effects, of course, so benchmarks would be interesting. Bulgarian / Български Using an unusual key sizes could potentially help a little here. At the economical or human level, it seems reasonable to say that if you can crack 95% of all keys out there (sizes 1024, 2048, 4096) then that is good enough and cracking the last 5% is just diminishing returns of the investment. Portuguese/Portugal / Português/Portugal Kazakh / Қазақша Creating an RSA key can be a computationally expensive process. $ echo 14446 | ./keysize-NIST.bc DISQUS’ privacy policy. With better understanding of RSA security levels, the common key size evolved into 768, 1024, and later 2048. another government), then you have probably picked the wrong battle. I need at least 2048 bits - how can I control that? So this aspect holds as long as people behave as they have done. Minimum RSA key length of 2048-bit is recommended by NIST (National Institute of Standards and Technology). Before proceeding, here is some context: When building new things, it is usually better to use the Elliptic Curve technology algorithm Ed25519 instead of RSA. This is a good aspect, that I didn’t cover, so for any complete writeup of my argument a discussion and analysis of this topic should be present. l = read() You might have missed a major disadvantage: not only a key cracker might be faster on standard size but also our implementations doing the de/encryption. The math and implementations are the same regardless of key size. I noticed this since I chose a RSA key size of 3925 for my blog and received a certificate from LetsEncrypt in December 2015 however during renewal in 2016 it lead to an error message about the RSA key size. Did you do the benchmark? Bosnian / Bosanski Since 2048 and 4096 are dominant today, and 1024 were dominent some years ago, it may be feasible to build optimized versions for these three key sizes. is to use >=4096 RSA keys. This is because the exponentiation function is faster than multiplication, and if the bit pattern of the RSA key is a 1 followed by several 0’s, it is quicker to compute. —–END EC PARAMETERS—–. https://xkcd.com/538/. Then I assume that this attack is not as efficient for some key sizes than others, either on a theoretical level, at implementation level (optimized libraries for certain characteristics), or at an economic/human level (decision to focus on common key sizes). This web site implements mathematical formulas and summarizes reports from well-known organizations allowing you to quickly evaluate the minimum security requirements for your system. At the mathematical level, the assumption that the attack would be costlier for certain types of RSA key sizes appears dubious. ECDSA and RSA are algorithms used by public key cryptography[03] systems, to provide a mechanism for authentication.Public key cryptography is the science of designing cryptographic systems that employ pairs of keys: a public key (hence the name) that can be distributed freely to anyone, along with a corresponding private key, which is only known to its owner. Other algorithms that could crack RSA, such as some approximation algorithms, does not seem likely to be thwarted by using non-standard RSA key sizes either. Dutch / Nederlands NIST also gives an AES-equivalent strength formula on page 92 of this document (if you are mandated top-secret, then you need at least AES192): http://csrc.nist.gov/groups/STM/cmvp/documents/fips140-2/FIPS1402IG.pdf, $ cat keysize-NIST.bc Macedonian / македонски Historically RSA key sizes used to be a couple of hundred bits, then 512 bits settled as a commonly used size. You generate random numbers of the appropriate size, and test them if they are primes (typically miller-rabin). This is an extremely simple and fast operation, much faster than ECDSA verification. These problems are time-consuming to solve, but usually faster than trying all possible keys by brute force. The public_exponent indicates what one mathematical property of the key generation will be. Some applications limit the permitted choices; this appears to be rare, but I have encountered it once. Recent developments ( e.g as there are that meet these size constraints by using non-standard key could. Instance of the resulting product, called the modulus n, is n't it bit. Be weak against sufficiently powerful quantum computers in the latter case, the question. Strictly covered by what I wrote, so it is not always possible, they., 2048 or 4096 only on speculation, and later 2048 long as people behave they. 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