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AUDIENCE COMMENTS
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CRYPTOGRAPHY
Marios - Cryptography
I am a student at Royal Holloway taking the Masters in Information Security. I have been taught by Fred Piper on Cyptography and he has again shown that such a subject is fascinating and can be understood by the masses. Thankyou you for the revision material Fred. Melvynn - slightly more time could have been used explaining crypto since the war and how it is used today.
Peter - Public Key Encryption
The description given about public key encryption being like a box being passed back and forth with padlocks being added and removed is misleading. A more acurate description would be a box with a lock that can be locked with one key, but needs another, completely different key to unlock it. Copies of the key that locks the box are made freely available, by the intended recipient, to anyone who asks - which is why this is known as the Public Key. The only key that can then open the box is kept very secure by the recipient and this is known as a Private Key.
Peter - Public Key Encryption
The secret to Public Key Encryption is that the encryption process uses modulus arithmatic and so what is transmitted is only the remainder of the equation. If you encrypt the letter "a" (ascii 97) by dividing it by a key value of say 5, the encrypted value is based on the modulus value which would be 2. However this encrypted value could just as easily come from "f" (ascii=102), "k" (107), "p" (112), etc (obviously, the ecryption process is more complex than this, but hopefully this demostrates the concept). This is why the public key cannot be used to decrypt the message it was used to encrypt as the process throws away too much information. The special relationship of the Public and Private keys (which themselves are derived from a complex equation) means that only the Private key can be used to decrypt the message. By using much larger keys, the chance of cracking a message using brute force becomes very difficult. The modulus aritmatic is also why the keys need to be prime numbers as otherwise the key's factors could be used to crack the code more easily.
Philip R Brenan, Cryptography
Public Key Encryption is based on Fermat's little theorem: a**p mod p = a (a is any number, p is prime, p > a) Examples: 2**3 mod 3 = 2 10**11 mod 11 = 10 By giving the public a number based on p, but with holding the complete value of p, a message can be encrypted and transmitted publicly, yet only the person who knows the exact value of p can decode the message in any reasonable amount of time. The public can only guess the remaining part of p, which is choosen large enough to make this task difficult with current technology. As Christopher remarks below, having split the prime p into two parts, either part can be given out publicly, as long as the other part is kept secret. Great program, incoherent panelists.
Mr. B McCann - Cryptography
Given the time available it’s a real shame that the programme did not allow sufficient time to explore in some detail the significant developments of public key cryptography. It would have been appropriate to highlight seminal works from Diffie-Hellman, Cocks & Ravist-Shamir-Adelman. Perhaps there might be the opportunity to produce a second programme focusing on such material.
Chris Miller - Public Key Encryption
Simon Singh's explanation of this subject using the analogy of the box with two padlocks was very useful, but it is only an analogy. In reality, the message is only sent once, encrypted with the 'public' key of the recipient who can then decrypt it with her private key. The public key can be (and to be useful should be) widely published - the private key must be kept strictly private (hence eliminating the key distribution problem referred to during the programme). Incidentally, the calculations necessary for public key cryptography are so lengthy that it is never used for encrypting an entire message. Instead a shared secret key is encrypted and transmitted using the public/private key method described above and then the secret key is used to send messages. Hope this helps!
Christopher - Public Key Encryption
I'd like to know the answer to the question below [stephen lovell's]. I've got another (I think related) confusion... If we think of encryption as a function to convert one number to another (each letter can be given a corresponding value) then we can represent alice's encrypting x as a(x), and bob's encrypting as b(x). Now we can represent alice's decrypting as a'(x), and bob's decrypting as b'(x). So here's the public key encryption process.. We have something - call it z. Alice encrypts it - we now have f(z). She sends it to Bob, who encrypts it - g(f(z)). He sends it back, and alice decrypts it - f'(g(f(z))). She sends it to bob who decrypts again - now we've got g'(f'(g(f(z)))). Now, if the message is restored to its original form, we should have the original z. This means g'(f'(g(f(z))))=z. Now, this is true in general only if f(g(x))=g(f(x)). So, here's my question: can we only use some functions for encryption (the ones that satisfy the latter condition)? If so, aren't these functions linear and easy to crack (by the method in stephen lovell's question)? [the reason I'm framing the question is because this is how I've been told we enrypt ascii text - f("a")=f(97)=99 for f(x)=x+2 because "a" is ascii 97] Anyway, please, somebody answer! I'm a bit confused!
Stephen Lovell - Public Key Encryption
If Alice sends Bob a message in code A which Bob then sends back in code (A+B), which Alice sends back in code (A+B-A=B), then Bob can read the original message in code (B-B=0). However if the message is intercepted all three times then the interceptor can calculate code A by comparing the second and third transmissions and hence decode the original transmission. How does the system remain secure?
In reply to HE Warr
The term you heard as "Xenography" is steganography.
Steve Lowman - padlocks
Awkward pacing and awkwardness, but at the end I was glad the radio had been out of reach. The explanation about the padlock in the box was the first time I understood this idea about modern encryption. Thanks.
R Green Cryptography
It was a great shame that Melvyn Bragg cut Professor Jardine short on the topic of the Jewish contribution to cryptography through Hebrew charaters. It would have been interesting
Cryptography
the radio programme appears to be on for 45 mins in the morning but when repeated on 30 mins according the prog listings - is this correct or is the repeat abridged and is the web listen again the 1st or the 2nd broadcast? A REPLY: The evening repeat is abridged to 30 minutes but the version on the website is the 45 minute morning edition.
Simpler Vigenere Cypher Explaination - Andy Pryke
A simpler way to explain the Vigenere cypher is to use a code word - say "ANDY". On one line you write your message, and underneath you write "ANDYANDYANDYANDY..." You then shift the letters in your messgae with "A" counting as "shift forward one letter" "B" meaning "shift forward 2 letters" etc. If a letter if shifted past the end of the alphabet, you wrap round, so for example "Y" + "C" means move on 3 ("C") letters from "Y". One letter on is "Z", 2 on is "A", 3 letters on gives us "B" Andy Pryke
D A Burke - Viginere Cipher
I have to question your contributer's statement that it took a 'genius' like Viginere to devise 'le chiffre indechiffrable', which is actually a fairly obvious extension of the Caesar cipher. Having invented it myself years ago, I am in a position to inform you that even a person of moderate intelligence is up to devising such a system, and Viginere probably wasn't the first to do so.
Nigel West on Cryptography
Your programme containe three verifiable errors of fact:- 1. One-Time Pads are not unbreakable. Actaully the German Foreign Ministry OTPs were broken throughout World War II. 2. Soviet codes did not 'betray the atomic spies'. Only Klaus Fuchs was identified from VENONA. Alan Nunn May was identified four years earlier, before any VENONA was read, having been named by Igor Gouzenko. 3. The Soviet cipher system was not compromised by the reuse of OTPs. The Soviets reused individual pages of the OTP.. not the same at all. 4. The asssertion that to read Enigma traffic possesion of a machine and the key was a prerequisite is entirely incorrect.
Mike O'Regan - Cryptography
There was a brief mention of "pseudo-random" during this programme. It would have helped if this aspect was explained. There are not many true "random" numbers used in life, whereas "pseudo-random" numbers abound. For instance, the numbers generated by ERNIE for Premium Bonds were said to have been "seeded" by the exact "real time" when they were drawn. Maybe a whole program could be devoted to random and pseudo-random numbers (or maybe it already has been done!)
Janice Smith : bungs and cryptography
Someone in the cryptography programme asked where the expression "to take a bung" comes from. I've always assumed that the modern "take a bung" derives from the cant term "bung" which could mean both "a purse" and also, rather confusingly, a criminal who steals purses. "Bung", "nip a bung" and "cuttle bung" are all to be found in Elizabethan and Jacobean sources, and would have been recognised as quite distinct from the contemporary "bung" which stopped barrels and helped the Babington plotters to send their encoded messages to Mary Queen of Scots. Lots of references for both meanings in the OED.
Peter Cunningham - Cyphers
The first 40 mins were an interesting review ... BUT you left out the 20th. century in terms of its overall contribution... 5 minutes is totally insufficient ! Thus it warrants another programme.... Please inform when ?? You discussed historical techniques (substitution etc) but it was the "likely" encoded content that provided a fascinating and alternative approach to code breaking; viz. it was partially responsible for undermining the Enigma codes... certainly the three wheel weather codes... and U-boat deployment in the N Atlantic. The book "The Enigma" by Robert Harris explains this quite well. Thus, today's programme needs a final chapter and thus should have another programme that more fully explores the 20th. Century's contribution to code breaking... I assume that the Enigma (in its own right) has been discussed before so should not more than say 35% of the programme's content... It leads directly onto the contribution made by "electronic computation" to coding algorithms and code breaking, and the concepts required by an electronic age to keep global information transmissions secure. I await to hear your considerations of the above. Fascinating !! PeterC/Reading/UK Please reply to >>> cyphers_radio4@peterc.nildram.co.uk Thank you.
Ray Murray
I have just listened, initially with interest and then in frustration, to "cryptography". The programme offered to link the early notions of cryptography with modern methods. The goal was never reached and listeners were unable to hear about truly modern methods such as those used in computer encryption or the potential of using the properties of photons in "quantum cryptography". This was due mainly to Melvyn Bragg's insistence that certain historical aspects of cryptography be adequately explained. In all cases the required mathematical intuition was limited and the programmed effectively "dumbed down" the content presumably because it was thought that the listener was stupid. The issue of the content of scientific or pseudo-scientific radio and television programmes should be reviewed by the BBC. If, by diluting the difficult concepts the programme makers hope to gain wider appeal they should realise that they are alienating many of the genuinely interested listeners.
Jim Russell - Cryptography
When I heard your introduction I thought that the subject was too big for a single programme, a thought that was confirmed by the truncated and confusing discussion of the current cryptographic technique that allows credit card details to be transmitted safely over the internet. I do not believe that it would have been understood by anyone who was not already aware of it. Can I suggest a second programme assuming, or very briefly summarising vigniere cyphers, and then dealing properly with the First World War battlefield cyphers as well as the Naval effort. You could also mention the possibility of attack on vigniere by isolating individual substitutions for frequency analysis. That is combine first, fourth, seventh and tenth letters and so on of the message; and the other sequences. On the other hand the first 30-35 minutes of the programme was one of the best explanations of the history of cryptography that I have come across. Regards J Russell
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