Low-Weight Primes for Lightweight Elliptic Curve Cryptography on 8-bit AVR Processors

Small 8-bit RISC processors and micro-controllers based on the AVR instruction set architecture are widely used in the embedded domain with applications ranging from smartcards over control systems to wireless sensor nodes. Many of these applications require asymmetric encryption or authentication, which has spurred a body of research into implementation aspects of Elliptic Curve Cryptography (ECC) on the AVR platform. In this paper, we study the suitability of a special class of finite fields, the so-called Optimal Prime Fields (OPFs), for a "lightweight" implementation of ECC with a view towards high performance and security. An OPF is a finite field Fp defined by a prime of the form p = u*2^k + v, whereby both u and v are "small" (in relation to 2^k) so that they fit into one or two registers of an AVR processor. OPFs have a low Hamming weight, which allows for a very efficient implementation of the modular reduction since only the non-zero words of p need to be processed. We describe a special variant of Montgomery multiplication for OPFs that does not execute any input-dependent conditional statements (e.g. branch instructions) and is, hence, resistant against certain side-channel attacks. When executed on an Atmel ATmega processor, a multiplication in a 160-bit OPF takes just 3237 cycles, which compares favorably with other implementations of 160-bit modular multiplication on an 8-bit processor. We also describe a performance-optimized and a security-optimized implementation of elliptic curve scalar multiplication over OPFs. The former uses a GLV curve and executes in 4.19M cycles (over a 160-bit OPF), while the latter is based on a Montgomery curve and has an execution time of approximately 5.93M cycles. Both results improve the state-of-the-art in lightweight ECC on 8-bit processors

Ruptured appendiceal cystadenoma presenting as right inguinal hernia in a patient with left colon cancer: A case report and review of literature

BACKGROUND: Mucoceles resulting from cystadenomas of the appendix are uncommon. Although rare, rupture of the mucoceles can occur with or without causing any abdominal complaint. There are several reports associating colonic malignancy with cystadenomas of the appendix. Herein, we report an unusual and interesting case of right inguinal hernia associated with left colon cancer. CASE PRESENTATION: A case of ruptured mucocele resulting from cystadenoma of the appendix was presented as right inguinal hernia in a 70-year-old male. The patient underwent colonoscopy, x-ray, ultrasound and computed tomography. Localized pseudomyxoma peritonei associated with adenocarcinoma of the descending colon was diagnosed. The patient underwent segmental resection of the colon, appendectomy, debridement of pseudomyxoma and closure of the internal ring of right inguinal canal. He is free of symptoms in one year follow-up. CONCLUSION: Synchronous colon cancer may occur in patients with appendiceal mucoceles. In such patients, the colon should be investigated and colonoscopy can be performed meticulously in cases of ruptured mucoceles and localized pseudomyxoma peritonei. Surgical intervention is the current choice of management

A Shuffle Argument Secure in the Generic Model

We propose a new random oracle-less NIZK shuffle argument. It has a simple structure, where the first verification equation ascertains that the prover has committed to a permutation matrix, the second verification equation ascertains that the same permutation was used to permute the ciphertexts, and the third verification equation ascertains that input ciphertexts were ``correctly\u27\u27 formed. The new argument has $3.5$ times more efficient verification than the up-to-now most efficient shuffle argument by Fauzi and Lipmaa (CT-RSA 2016). Compared to the Fauzi-Lipmaa shuffle argument, we (i) remove the use of knowledge assumptions and prove our scheme is sound in the generic bilinear group model, and (ii) prove standard soundness, instead of culpable soundness

Challenges with Assessing the Impact of NFS Advances on the Security of Pairing-based Cryptography

In the past two years there have been several advances in Number Field Sieve (NFS) algorithms for computing discrete logarithms in finite fields $\mathbb{F}_{p^n}$ where $p$ is prime and $n > 1$ is a small integer. This article presents a concise overview of these algorithms and discusses some of the challenges with assessing their impact on keylengths for pairing-based cryptosystems

Compact Structure-preserving Signatures with Almost Tight Security

In structure-preserving cryptography, every building block shares the same bilinear groups. These groups must be generated for a specific, a prior fixed security level, and thus it is vital that the security reduction of all involved building blocks is as tight as possible. In this work, we present the first generic construction of structure-preserving signature schemes whose reduction cost is independent of the number of signing queries. Its chosen-message security is almost tightly reduced to the chosen-plaintext security of a structure-preserving public-key encryption scheme and the security of Groth-Sahai proof system. Technically, we adapt the adaptive partitioning technique by Hofheinz (Eurocrypt 2017) to the setting of structure-preserving signature schemes. To achieve a structure-preserving scheme, our new variant of the adaptive partitioning technique relies only on generic group operations in the scheme itself. Interestingly, however, we will use non-generic operations during our security analysis. Instantiated over asymmetric bilinear groups, the security of our concrete scheme is reduced to the external Diffie-Hellman assumption with linear reduction cost in the security parameter, independently of the number of signing queries. The signatures in our schemes consist of a larger number of group elements than those in other non-tight schemes, but can be verified faster, assuming their security reduction loss is compensated by increasing the security parameter to the next standard level

Function-Hiding Inner Product Encryption is Practical

In a functional encryption scheme, secret keys are associated with functions and ciphertexts are associated with messages. Given a secret key for a function f, and a ciphertext for a message x, a decryptor learns f(x) and nothing else about x. Inner product encryption is a special case of functional encryption where both secret keys and ciphertext are associated with vectors. The combination of a secret key for a vector x and a ciphertext for a vector y reveal and nothing more about y. An inner product encryption scheme is function- hiding if the keys and ciphertexts reveal no additional information about both x and y beyond their inner product. In the last few years, there has been a flurry of works on the construction of function-hiding inner product encryption, starting with the work of Bishop, Jain, and Kowalczyk (Asiacrypt 2015) to the more recent work of Tomida, Abe, and Okamoto (ISC 2016). In this work, we focus on the practical applications of this primitive. First, we show that the parameter sizes and the run-time complexity of the state-of-the-art construction can be further reduced by another factor of 2, though we compromise by proving security in the generic group model. We then show that function privacy enables a number of applications in biometric authentication, nearest-neighbor search on encrypted data, and single-key two-input functional encryption for functions over small message spaces. Finally, we evaluate the practicality of our encryption scheme by implementing our function-hiding inner product encryption scheme. Using our construction, encryption and decryption operations for vectors of length 50 complete in a tenth of a second in a standard desktop environment